%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.28",
%%%     date            = "10 October 2024",
%%%     time            = "07:35:07 MDT",
%%%     filename        = "agm.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     FAX             = "+1 801 581 4148",
%%%     URL             = "https://www.math.utah.edu/~beebe",
%%%     checksum        = "07030 13309 56396 568331",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "arithmetic--geometric mean; bibliography;
%%%                        BibTeX; geometric--arithmetic mean",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of publications about
%%%                        the arithmetic--geometric mean (AGM)
%%%                        iteration, discovered by Lagrange before
%%%                        1785, and independently by Carl Friedrich
%%%                        Gauss (1777--1855) in 1799.  Adrien-Marie
%%%                        Legendre (1752--1833) discovered a relation
%%%                        between certain elliptic integrals that led
%%%                        Gauss to apply the AGM to the calculation of
%%%                        the mathematical constant pi.
%%%
%%%                        However, the AGM's first well-known
%%%                        applications, to the high-precision
%%%                        computation of pi, and of high-precision
%%%                        computation of elementary and elliptic
%%%                        functions, were not published until 1971 and
%%%                        1976 (see entries Carlson:1971:AIA,
%%%                        Brent:1976:FMP, and Salamin:1976:CUA).  There
%%%                        was earlier work in the 1920s (see the books
%%%                        and papers by Louis V. King) using the AGM to
%%%                        compute Jacobian elliptic functions, but
%%%                        King's publications seem not to have been
%%%                        widely known or appreciated.
%%%
%%%                        Gauss' work is better known, and the AGM is
%%%                        often (improperly) credited to him alone; see
%%%                        entry Gauss:1992:AGM for a Spanish
%%%                        translation of his original work, from the
%%%                        first publication in the original Latin in
%%%                        his collected works (entry Werke Vol. X-1
%%%                        (1917)).
%%%
%%%                        The AGM provides an iterative process for
%%%                        computing various constants and functions,
%%%                        often with quadratric convergence.  Unlike
%%%                        Newton--Raphson iteration, the AGM process is
%%%                        not self correcting: errors accumulate with
%%%                        each iteration.  That is a disadvantage with
%%%                        hardware arithmetic of fixed precision, but
%%%                        is easily handled in software
%%%                        multiple-precision arithmetic by computing
%%%                        with a few more digits than are eventually
%%%                        needed.  The AGM iteration is comparatively
%%%                        simple to program, and especially for
%%%                        arbitrary-precision arithmetic, provides a
%%%                        convenient way to compute several important
%%%                        constants and functions.
%%%
%%%                        Since the mid-1990s, in a few cases, variants
%%%                        of the AGM have been discovered possessing
%%%                        convergence of order 3, 4, 5, ..., 9.  For
%%%                        example, pi can be calculated to a thousand
%%%                        million digits with only ten 9-th order AGM
%%%                        iterations.
%%%
%%%                        At version 1.28, the year coverage looked
%%%                        like this:
%%%
%%%                             1866 (   1)    1919 (   0)    1972 (   4)
%%%                             1868 (   1)    1921 (   1)    1974 (   0)
%%%                             1869 (   0)    1922 (   0)    1975 (   2)
%%%                             1870 (   0)    1923 (   0)    1976 (   7)
%%%                             1871 (   0)    1924 (   1)    1977 (   2)
%%%                             1872 (   0)    1925 (   0)    1978 (   5)
%%%                             1873 (   0)    1926 (   0)    1979 (   3)
%%%                             1874 (   0)    1927 (   1)    1980 (   1)
%%%                             1875 (   0)    1928 (   1)    1981 (   3)
%%%                             1876 (   0)    1929 (   0)    1982 (   2)
%%%                             1877 (   0)    1930 (   0)    1983 (   3)
%%%                             1878 (   0)    1931 (   0)    1984 (   6)
%%%                             1879 (   0)    1932 (   0)    1985 (   3)
%%%                             1880 (   0)    1933 (   0)    1986 (   5)
%%%                             1881 (   0)    1934 (   0)    1987 (  10)
%%%                             1882 (   0)    1935 (   0)    1988 (  22)
%%%                             1883 (   0)    1936 (   1)    1989 (   8)
%%%                             1884 (   0)    1937 (   0)    1990 (   9)
%%%                             1885 (   0)    1938 (   0)    1991 (   8)
%%%                             1886 (   0)    1939 (   0)    1992 (   9)
%%%                             1887 (   0)    1940 (   0)    1993 (  13)
%%%                             1888 (   0)    1941 (   0)    1994 (  12)
%%%                             1889 (   0)    1942 (   1)    1995 (  12)
%%%                             1890 (   0)    1943 (   0)    1996 (  15)
%%%                             1891 (   0)    1944 (   1)    1997 (  17)
%%%                             1892 (   0)    1945 (   1)    1998 (   8)
%%%                             1893 (   0)    1946 (   1)    1999 (  13)
%%%                             1894 (   0)    1947 (   0)    2000 (  12)
%%%                             1895 (   0)    1948 (   0)    2001 (   6)
%%%                             1896 (   0)    1949 (   0)    2002 (   6)
%%%                             1897 (   0)    1950 (   0)    2003 (  14)
%%%                             1898 (   0)    1951 (   0)    2004 (  11)
%%%                             1899 (   0)    1952 (   0)    2005 (   2)
%%%                             1900 (   0)    1953 (   0)    2006 (   9)
%%%                             1901 (   0)    1954 (   0)    2007 (   9)
%%%                             1902 (   0)    1955 (   0)    2008 (  11)
%%%                             1903 (   0)    1956 (   3)    2009 (   9)
%%%                             1904 (   0)    1957 (   0)    2010 (  13)
%%%                             1905 (   0)    1958 (   1)    2011 (  19)
%%%                             1906 (   0)    1959 (   0)    2012 (  20)
%%%                             1907 (   0)    1960 (   1)    2013 (  16)
%%%                             1908 (   0)    1961 (   0)    2014 (  16)
%%%                             1909 (   0)    1962 (   0)    2015 (  15)
%%%                             1910 (   0)    1963 (   3)    2016 (  26)
%%%                             1911 (   1)    1964 (   0)    2017 (  13)
%%%                             1912 (   0)    1965 (   3)    2018 (   3)
%%%                             1913 (   0)    1966 (   3)    2019 (   1)
%%%                             1914 (   0)    1967 (   3)    2020 (   6)
%%%                             1915 (   0)    1968 (   4)    2021 (   0)
%%%                             1916 (   0)    1969 (   1)    2022 (   2)
%%%                             1917 (   1)    1970 (   4)    2023 (   2)
%%%                             1918 (   0)    1971 (   6)    2024 (   1)
%%%
%%%                             Article:        393
%%%                             Book:            15
%%%                             InCollection:    36
%%%                             InProceedings:    7
%%%                             Misc:             2
%%%                             PhdThesis:        2
%%%                             Proceedings:      7
%%%                             TechReport:       8
%%%                             Unpublished:     19
%%%
%%%                             Total entries:  489
%%%
%%%                        Data for this entry have been collected from
%%%                        the BibNet Project and TeX User Group
%%%                        bibliography archives, and the arXiv.org,
%%%                        Elsevier ScienceDirect, MathSciNet, Springer
%%%                        Link, and Wiley Online databases.
%%%
%%%                        In this bibliography, entries are sorted
%%%                        first by ascending year, and within each
%%%                        year, alphabetically by author or editor,
%%%                        and then, if necessary, by the 3-letter
%%%                        abbreviation at the end of the BibTeX
%%%                        citation tag, using the bibsort -byyear
%%%                        utility.  Year order has been chosen to
%%%                        make it easier to identify the most recent
%%%                        work.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================

@Preamble{
    "\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" #
    "\ifx \undefined \mathbb    \def \mathbb    #1{{\bf #1}}  \fi"#
    "\def \cprime {$'$}" #
    "\hyphenation{ }"
}

%%% ====================================================================
%%% Institutional abbreviations:

@String{inst-CECM               = "Centre for Experimental and Constructive
                                  Mathematics (CECM) at Simon Fraser
                                  University (SFU)"}
@String{inst-CECM:adr           = "Burnaby, BC V5A 1S6, Canada"}

@String{inst-STAN-CS            = "Stanford University, Department of
                                  Computer Science"}
@String{inst-STAN-CS:adr        = "Stanford, CA, USA"}

%%% ====================================================================
%%% Journal abbreviations:

@String{j-ABSTR-APPL-ANAL       = "Abstract and Applied Analysis"}

@String{j-ACTA-GEOD-GEOPHYS-HU  = "Acta Geodaetica et Geophysica Hungarica"}

@String{j-ADV-APPL-STAT         = "Advances and Applications in Statistics"}

@String{j-ADV-COMPUT-MATH       = "Advances in Computational Mathematics"}

@String{j-ADV-MATH              = "Advances in Mathematics"}

@String{j-AEQUATIONES-MATHEMATICAE = "Aequationes Mathematicae"}

@String{j-AMER-J-PHYSICS        = "American Journal of Physics"}

@String{j-AMER-MATH-MONTHLY     = "American Mathematical Monthly"}

@String{j-AMER-STAT             = "The American Statistician"}

@String{j-ANN-FUNCT-ANAL        = "Annals of Functional Analysis"}

@String{j-ANN-SC-NORM-SUPER-PISA-CL-SCI = "Annali della Scuola normale
                                  superiore di Pisa, Classe di scienze"}

@String{j-APPL-MATH-COMP        = "Applied Mathematics and Computation"}

@String{j-APPL-MATH-LETT        = "Applied Mathematics Letters"}

@String{j-APPL-MATH-MODEL       = "Applied Mathematical Modelling"}

@String{j-APPL-MATH-SCI-RUSE    = "Applied Mathematical Sciences (Ruse)"}

@String{j-ARCH-INEQUAL-APPL     = "Archives of Inequalities and Applications."}

@String{j-AUSTRALIAN-MATH-SOC-GAZ = "Australian Mathematical Society Gazette"}

@String{j-BOLL-STOR-SCI-MAT     = "Bollettino di Storia delle Scienze Matematiche"}

@String{j-BULL-AUSTRAL-MATH-SOC = "Bulletin of the Australian Mathematical Society"}

@String{j-BULL-LOND-MATH-SOC    = "Bulletin of the London Mathematical Society"}

@String{j-C-R-ACAD-SCI-I        = "Comptes rendus de l'Acad{\'e}mie des
                                  sciences. S{\'e}rie I, Math{\'e}matique"}

@String{j-CAN-MATH-BULL         = "Bulletin canadien de
                                  math\-{\'e}\-mat\-iques = Canadian
                                  Mathematical Bulletin"}

@String{j-COLLEGE-MATH-J        = "College Mathematics Journal"}

@String{j-COMMUN-KOREAN-MATH-SOC = "Communications of the Korean Mathematical
                                  Society"}

@String{j-COMPUT-MATH-APPL      = "Computers and Mathematics with
                                  Applications"}

@String{j-COMPUTERS-AND-GRAPHICS = "Computers and Graphics"}

@String{j-CONG-NUM              = "Congressus Numerantium"}

@String{j-CONST-APPROX          = "Constructive Approximation"}

@String{j-CWI-QUARTERLY         = "CWI Quarterly"}

@String{j-DEUTSCH-MATH-V        = "Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)"}

@String{j-ECON-QUAL-CONTROL     = "Economic Quality Control"}

@String{j-ELEM-MATH             = "Elemente der Mathematik"}

@String{j-ENSEIGN-MATH-2        = "L'Enseignement Math{\'e}matique. Revue
                                  Internationale. 2e S{\'e}rie"}

@String{j-EUR-J-COMB            = "European Journal of Combinatorics"}

@String{j-EXP-MATH              = "Experimental Mathematics"}

@String{j-EXPO-MATH             = "Expositiones Mathematicae"}

@String{j-FIB-QUART             = "Fibonacci Quarterly"}

@String{j-FUNCT-SPACES          = "Journal of Function Spaces"}

@String{j-GAZ-MATH              = "Gazette des Math{\'e}maticiens"}

@String{j-HOKKAIDO-MATH-J       = "Hokkaido Mathematical Journal"}

@String{j-IMA-J-NUMER-ANAL      = "IMA Journal of Numerical Analysis"}

@String{j-INDIAN-J-MATH         = "Indian Journal of Mathematics"}

@String{j-INT-J-MATH            = "International Journal of Mathematics"}

@String{j-INT-J-MATH-EDU-SCI-TECH = "International Journal of Mathematical
                                  Education in Science and Technology"}

@String{j-INT-J-MATH-MATH-SCI   = "International Journal of Mathematics and
                                  Mathematical Sciences"}

@String{j-INT-J-NUMBER-THEORY   = "International Journal of Number Theory"}

@String{j-INT-J-PROD-ECON       = "International Journal of Production
                                  Economics"}

@String{j-INT-J-PURE-APPL-MATH  = "International Journal of Pure and Applied
                                  Mathematics"}

@String{j-INT-J-SYST-SCI        = "International Journal of Systems Science"}

@String{j-INTERDISCIP-INFORM-SCI = "Interdisciplinary Information Sciences"}

@String{j-IRISH-MATH-SOC-BULL   = "Irish Mathematical Society Bulletin"}

@String{j-ISRAEL-J-MATH         = "Israel Journal of Mathematics"}

@String{j-ITAL-J-PURE-APPL-MATH = "Ital. J. Pure Appl. Math."}

@String{j-J-ACM                 = "Journal of the ACM"}

@String{j-J-AM-STAT-ASSOC       = "Journal of the American Statistical
                                  Association"}

@String{j-J-APPL-MATH           = "Journal of Applied Mathematics"}

@String{j-J-APPROX-THEORY       = "Journal of Approximation Theory"}

@String{j-J-AUTOM-REASON        = "Journal of Automated Reasoning"}

@String{j-J-COMPUT-APPL-MATH    = "Journal of Computational and Applied
                                  Mathematics"}

@String{j-J-ELECTROST           = "Journal of Electrostatics"}

@String{j-J-FUNCT-ANAL          = "Journal of functional analysis"}

@String{j-J-INEQUAL-APPL        = "Journal of Inequalities and Applications"}

@String{j-J-LOND-MATH-SOC       = "Journal of the London Mathematical Society"}

@String{j-J-LOND-MATH-SOC-2     = "Journal of the London Mathematical Society.
                                  Second Series"}

@String{j-J-MATH-ANAL-APPL      = "Journal of Mathematical Analysis and
                                  Applications"}

@String{j-J-MATH-INEQUAL        = "Journal of Mathematical Inequalities"}

@String{j-J-MATH-PHYS           = "Journal of Mathematical Physics"}

@String{j-J-MATH-SCI-ADV-APPL   = "Journal of Mathematical Sciences. Advances
                                  and Applications"}

@String{j-J-NUMBER-THEORY       = "Journal of Number Theory"}

@String{j-J-THEOR-PROBAB        = "Journal of Theoretical Probability"}

@String{j-JIPAM-J-INEQUAL-PURE-APPL-MATH = "IPAM. Journal of Inequalities in
                                  Pure and Applied Mathematics"}

@String{j-LECT-NOTES-COMP-SCI   = "Lecture Notes in Computer Science"}

@String{j-LECT-NOTES-MATH       = "Lecture Notes in Mathematics"}

@String{j-LIN-MULT-ALGEBRA      = "Linear Multilinear Algebra"}

@String{j-LIN-AND-MULT-ALGEBRA  = "Linear and Multilinear Algebra"}

@String{j-LINEAR-ALGEBRA-APPL   = "Linear Algebra and its Applications"}

@String{j-MAPLE-TECH-NEWS       = "Maple Technical Newsletter"}

@String{j-MATH-ANN              = "Mathematische Annalen"}

@String{j-MATH-COMPUT           = "Mathematics of Computation"}

@String{j-MATH-GAZ              = "The Mathematical Gazette"}

@String{j-MATH-INEQUAL-APPL     = "Mathematical Inequalities \& Applications"}

@String{j-MATH-INTEL            = "The Mathematical Intelligencer"}

@String{j-MATH-MAG              = "Mathematics Magazine"}

@String{j-MATH-NACHR            = "Mathematische Nachrichten"}

@String{j-MATH-PROC-CAMB-PHILOS-SOC = "Mathematical Proceedings of the
                                  Cambridge Philosophical Society"}

@String{j-MATH-STUDENT          = "The Mathematics Student"}

@String{j-NAMS                  = "Notices of the American Mathematical
                                  Society"}

@String{j-NIEUW-ARCHIEF-WISKUNDE-4 = "Nieuw Archief voor Wiskunde. Vierde Serie"}

@String{j-NORDISK-MATH-TIDSKR   = "Nordisk Matematisk Tidskrift"}

@String{j-NUM-MATH              = "Numerische Mathematik"}

@String{j-NUMER-FUNCT-ANAL-OPTIM = "Numerical Functional Analysis and
                                  Optimization"}

@String{j-OBZORNIK-MAT-FIZ      = "Obzornik Mat. Fiz."}

@String{j-OCTOGON-MATH-MAG      = "Octogon Mathematical Magazine"}

@String{j-OPER-MATRICES         = "Operators and Matrices"}

@String{j-PAC-J-APPL-MATH       = "Pacific Journal of Applied Mathematics"}

@String{j-PAC-J-MATH            = "Pacific Journal of Mathematics"}

@String{j-PHYS-LET-A            = "Physics Letters A"}

@String{j-PI-MU-EPSILON-J       = "Pi Mu Epsilon Journal"}

@String{j-PROC-AM-MATH-SOC      = "Proceedings of the American Mathematical
                                  Society"}

@String{j-PROC-JAPAN-ACAD-SER-A-MATH-SCI = "Proceedings of the Japan Academy of
                                  Sciences. Series A. Mathematical Sciences"}

@String{j-PROC-R-SOC-EDINB-SECT-A-MATH = "Proceedings of the Royal Society of
                                  Edinburgh. Section A, Mathematical and
                                  Physical Sciences"}

@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS = "Proceedings of the Royal Society of
                                  London. Series A, Containing Papers of a
                                  Mathematical and Physical Character"}

@String{j-PUBL-MATH-DEBRECEN    = "Publicationes Mathematicae Debrecen"}

@String{j-RAMANUJAN-J           = "The {Ramanujan} Journal"}

@String{j-REND-CIRC-MAT         = "Rendiconti del Circolo matematico di
                                  Palermo"}

@String{j-RESONANCE             = "Resonance"}

@String{j-ROCKY-MOUNTAIN-J-MATH = "Rocky Mountain Journal of Mathematics"}

@String{j-SCI-MATH-JPN          = "Scientiae Mathematicae Japonicae"}

@String{j-SIAM-J-APPL-MATH      = "SIAM Journal on Applied Mathematics"}

@String{j-SIAM-J-MAT-ANA-APPL   = "SIAM Journal on Matrix Analysis and
                                  Applications"}

@String{j-SIAM-J-MATH-ANA       = "SIAM Journal on Mathematical Analysis"}

@String{j-SIAM-J-OPT            = "SIAM Journal on Optimization"}

@String{j-SIAM-REVIEW           = "SIAM Review"}

@String{j-STAT-PROB-LETT        = "Statistics \& Probability Letters"}

@String{j-STOCH-PROC-APPL       = "Stochastic Processes and Their
                                  Applications"}

@String{j-TAMKANG-J-MATH        = "Tamkang Journal of Mathematics"}

@String{j-TOPOLOGY              = "Topology"}

@String{j-TRANS-AM-MATH-SOC     = "Transactions of the American Mathematical
                                  Society"}

@String{j-TWO-YEAR-COLL-MATH-J  = "Two-Year College Mathematics Journal"}

@String{j-UTIL-MATH             = "Utilitas Mathematica"}

@String{j-Z-ANGE-MATH-MECH      = "{Zeitschrift f{\"u}r Angewandte Mathematik
                                  und Mechanik}"}

@String{j-ZH-VYCHISL-MAT-MAT-FIZ = "Zhurnal Vychislitel'no{u{i}} Matematiki i
                                  Matematichesko{u{i}} Fiziki"}

%%% ====================================================================
%%% Publisher abbreviations:

@String{pub-ACADEMIC            = "Academic Press"}
@String{pub-ACADEMIC:adr        = "New York, NY, USA"}

@String{pub-CAMBRIDGE           = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr       = "Cambridge, UK"}

@String{pub-IEEE                = "IEEE Computer Society Press"}
@String{pub-IEEE:adr            = "1109 Spring Street, Suite 300,
                                  Silver Spring, MD 20910, USA"}

@String{pub-SV                  = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg,
                                  Germany~/ London, UK~/ etc."}

@String{pub-WILEY               = "Wiley"}
@String{pub-WILEY:adr           = "New York, NY, USA"}

%%% ====================================================================
%%% BibTeX entries, sorted by year, and then by citation label:

@Book{Gauss:1866:W,
  author =       "Carl Friedrich Gauss",
  title =        "Werke",
  volume =       "3",
  publisher =    "Koniglichen Gesellschaft der Wissenschaften",
  address =      "G{\"o}ttingen, Germany",
  pages =        "????",
  year =         "1866",
  bibdate =      "Tue Mar 14 19:03:18 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1777--1855",
  remark =       "See pages 361--403 for AGM work.",
}

@InCollection{Lagrange:1868:X,
  author =       "Joseph-Louis Lagrange",
  booktitle =    "{\OE}uvres. ({French}) [{Works}]",
  title =        "????",
  publisher =    "Gauthier-Villars",
  address =      "Paris, France",
  pages =        "253--312",
  year =         "1868",
  bibdate =      "Tue Mar 14 18:45:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1736--1813",
  language =     "French",
  remark =       "See especially pages 267 and 272.",
}

@Article{Schlesinger:1911:GJA,
  author =       "L. Schlesinger",
  title =        "{{\"U}ber Gauss' Jugendarbeiten zum
                 arithmetisch--geometrischen Mittel}. ({German}) [{On}
                 {Gauss}' youthful work on the arithmetic--geometric
                 mean]",
  journal =      j-DEUTSCH-MATH-V,
  volume =       "20",
  number =       "??",
  pages =        "396--403",
  month =        "????",
  year =         "1911",
  bibdate =      "Tue Mar 14 18:38:44 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  ZMnumber =     "42.0466.01",
  acknowledgement = ack-nhfb,
  ajournal =     "Jber. Deutsch. Math.--Verein",
  fjournal =     "Jahresbericht der Deutschen Mathematiker-Vereinigung
                 (DMV)",
  language =     "German",
}

@InCollection{Gauss:1917:OPG,
  author =       "Carl Friedrich Gauss",
  booktitle =    "Werke",
  title =        "De origene propietatibusque generalibus numerorum
                 mediorum aritmet. geometricorum. ({Latin}) []",
  volume =       "X-1",
  publisher =    "Koniglichen Gesellschaft der Wissenschaften",
  address =      "G{\"o}ttingen, Germany",
  pages =        "??--??",
  year =         "1917",
  bibdate =      "Tue Mar 14 17:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1777--1855",
  language =     "Latin",
  remark =       "This work was not published during Gauss's lifetime
                 (1777--1855).",
}

@Article{King:1921:SNF,
  author =       "Louis Vessot King",
  title =        "On Some New Formulae for the Numerical Calculation of
                 the Mutual Induction of Coaxial Circles",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS,
  volume =       "100",
  number =       "702",
  pages =        "60--66",
  day =          "4",
  month =        oct,
  year =         "1921",
  DOI =          "https://doi.org/10.1098/rspa.1921.0070",
  ISSN =         "0950-1207 (print), 2053-9150 (electronic)",
  bibdate =      "Wed Feb 03 09:07:10 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  note =         "This is the first known publication of the AGM method,
                 discovered by the author in 1913, for computing
                 Jacobian elliptic functions. See also
                 \cite{King:1924:DNC,King:2007:DNC}.",
  URL =          "http://www.jstor.org/stable/93861",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society of London. Series A,
                 Containing Papers of a Mathematical and Physical
                 Character",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
}

@Book{King:1924:DNC,
  author =       "Louis Vessot King",
  title =        "On the Direct Numerical Calculation of Elliptic
                 Functions and Integrals",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "viii + 42",
  year =         "1924",
  LCCN =         "QA343",
  bibdate =      "Wed Feb 03 08:53:04 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  remark =       "The AGM method for Jacobian elliptic functions was
                 discovered by this book's author at McGill University
                 in 1913, first published in \cite{King:1921:SNF}, and
                 then in this monograph (reprinted in
                 \cite{King:2007:DNC}).",
}

@Article{Huntington:1927:SIP,
  author =       "Edward V. Huntington",
  title =        "Sets of independent postulates for the arithmetic
                 mean, the geometric mean, the harmonic mean, and the
                 root-mean-square",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "29",
  number =       "1",
  pages =        "1--22",
  year =         "1927",
  CODEN =        "TAMTAM",
  DOI =          "https://doi.org/10.2307/1989276",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "26D15",
  MRnumber =     "1501374",
  bibdate =      "Tue Aug 15 11:29:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/tran/",
}

@Article{Geppert:1928:TAG,
  author =       "Harald Geppert",
  title =        "{Zur Theorie des arithmetisch--geometrischen Mittels}.
                 ({German}) [{On} the theory of the
                 arithmetic--geometric mean]",
  journal =      j-MATH-ANN,
  volume =       "99",
  number =       "1",
  pages =        "162--180",
  month =        dec,
  year =         "1928",
  CODEN =        "MAANA3",
  DOI =          "https://doi.org/10.1007/BF01459092",
  ISSN =         "0025-5831 (print), 1432-1807 (electronic)",
  ISSN-L =       "0025-5831",
  bibdate =      "Tue Mar 14 18:33:51 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/article/10.1007/BF01459092",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Annalen",
  journal-URL =  "http://link.springer.com/journal/208",
  language =     "German",
  received =     "04 March 1927",
}

@PhdThesis{Butter:1936:CTA,
  author =       "Franklin A. {Butter, Jr.}",
  title =        "A Contribution to the Theory of the
                 Arithmetic--Geometric Mean",
  type =         "Thesis ({Ph.D.})",
  school =       "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  year =         "1936",
  MRnumber =     "2937121",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://search.proquest.com/docview/301788817",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Rauch:1942:MPS,
  author =       "Stanley Eugene Rauch",
  title =        "Mapping properties of the second arithmetic mean of
                 the geometric series",
  type =         "Thesis ({Ph.D.})",
  school =       "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  year =         "1942",
  MRnumber =     "2937549",
  bibdate =      "Tue Aug 15 11:29:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://search.proquest.com/docview/301867689",
  acknowledgement = ack-nhfb,
}

@Article{Stubban:1944:AGM,
  author =       "John Olav Stubban",
  title =        "On the arithmetic and geometric means",
  journal =      "Norsk Mat. Tidsskr.",
  volume =       "26",
  pages =        "116--117",
  year =         "1944",
  MRclass =      "27.0X",
  MRnumber =     "0017777",
  bibdate =      "Tue Aug 15 11:29:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Aiyer:1945:AGM,
  author =       "S. Janardana Aiyer",
  title =        "On the arithmetic and the geometric means from a type
                 {III} population",
  journal =      j-MATH-STUDENT,
  volume =       "13",
  pages =        "11--15",
  year =         "1945",
  CODEN =        "MTHSBH",
  ISSN =         "0025-5742",
  MRclass =      "62.0X",
  MRnumber =     "0013881",
  bibdate =      "Tue Aug 15 11:29:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematics Student",
}

@Article{Nanjundiah:1946:IRA,
  author =       "T. S. Nanjundiah",
  title =        "Inequalities relating to arithmetic and geometric
                 means. {I}, {II}",
  journal =      "Half-Yearly J. Mysore Univ. Sect. B., N.S.",
  volume =       "6",
  pages =        "63--77, 107--113",
  year =         "1946",
  MRclass =      "27.0X",
  MRnumber =     "0044588",
  MRreviewer =   "E. F. Beckenbach",
  bibdate =      "Tue Aug 15 11:29:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bellman:1956:AGM,
  author =       "Richard Bellman",
  title =        "On the arithmetic--geometric mean inequality",
  journal =      j-MATH-STUDENT,
  volume =       "24",
  pages =        "233--234 (1957)",
  year =         "1956",
  CODEN =        "MTHSBH",
  ISSN =         "0025-5742",
  MRclass =      "09.2X",
  MRnumber =     "0085208",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematics Student",
  zzbibdate =    "Tue Aug 15 11:29:11 2017",
}

@Article{Hunter:1956:GIA,
  author =       "John Hunter",
  title =        "A generalization of the inequality of the
                 arithmetic--geometric means",
  journal =      "Proc. Glasgow Math. Assoc.",
  volume =       "2",
  pages =        "149--158",
  year =         "1956",
  MRclass =      "10.2X",
  MRnumber =     "0075984",
  MRreviewer =   "Harvey Cohn",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  zzbibdate =    "Tue Aug 15 11:29:11 2017",
}

@Article{Torrent:1956:NEC,
  author =       "J. Maj{\'o} Torrent",
  title =        "Note on the extension to the complex field of the
                 arithmetic and the geometric mean",
  journal =      "Gac. Mat., Madrid (1)",
  volume =       "8",
  pages =        "195--198",
  year =         "1956",
  MRclass =      "09.2X",
  MRnumber =     "0085209",
  bibdate =      "Tue Aug 15 11:29:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kober:1958:AGM,
  author =       "H. Kober",
  title =        "On the arithmetic and geometric means and on
                 {H{\"o}lder}'s inequality",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "9",
  pages =        "452--459",
  year =         "1958",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.2307/2033003",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "26.00",
  MRnumber =     "0093564",
  MRreviewer =   "T. M. Apostol",
  bibdate =      "Tue Aug 15 11:29:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@Article{Diananda:1960:CNS,
  author =       "P. H. Diananda",
  title =        "Classroom Notes: a Simple Proof of the Arithmetic Mean
                 Geometric Mean Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "67",
  number =       "10",
  pages =        "1007--1007",
  month =        dec,
  year =         "1960",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2309236",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRnumber =     "1531004",
  bibdate =      "Mon Jun 28 12:36:07 MDT 1999",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Akerberg:1963:CNP,
  author =       "Bengt Akerberg",
  title =        "Classroom Notes: A Proof of the Arithmetic--Geometric
                 Mean Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "70",
  number =       "9",
  pages =        "997--998",
  month =        nov,
  year =         "1963",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2313068",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "Contributed Item",
  MRnumber =     "1532378",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Everitt:1963:IGA,
  author =       "W. N. Everitt",
  title =        "On an Inequality for the Generalized Arithmetic and
                 Geometric Means",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "70",
  number =       "3",
  pages =        "251--255",
  month =        mar,
  year =         "1963",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:37:02 MDT 1999",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Wilf:1963:SAI,
  author =       "Herbert S. Wilf",
  title =        "Some applications of the inequality of arithmetic and
                 geometric means to polynomial equations",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "14",
  pages =        "263--265",
  year =         "1963",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.2307/2034624",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "30.10",
  MRnumber =     "0145047",
  MRreviewer =   "O. Shisha",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@Article{Oppenheim:1965:ICA,
  author =       "Alexander Oppenheim",
  title =        "On inequalities connecting arithmetic means and
                 geometric means of two sets of three positive numbers",
  journal =      j-MATH-GAZ,
  volume =       "49",
  pages =        "160--162",
  year =         "1965",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.2307/3612307",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  MRclass =      "26.70",
  MRnumber =     "0185063",
  MRreviewer =   "H. Burkill",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}

@Book{Pars:1965:TAD,
  author =       "Leopold Alexander Pars",
  title =        "A Treatise on Analytical Dynamics",
  publisher =    "Heinemann",
  address =      "London, UK",
  pages =        "xxi + 641",
  year =         "1965",
  bibdate =      "Wed Mar 15 08:09:52 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Tricomi:1965:SID,
  author =       "F. G. Tricomi",
  title =        "Sull'algoritmo iterativo del {Borchardt} e su di una
                 sua generalizzazione. ({Italian}) [{On} the iterative
                 algorithm of {Borchardt} and on one of its
                 generalization]",
  journal =      j-REND-CIRC-MAT,
  volume =       "2",
  number =       "14",
  pages =        "85--94",
  month =        "????",
  year =         "1965",
  CODEN =        "RCMMAR",
  ISSN =         "0009-725X (print), 1973-4409 (electronic)",
  ISSN-L =       "0009-725X",
  bibdate =      "Tue Mar 14 18:46:58 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rendiconti del Circolo matematico di Palermo",
}

@Article{Mitrinovic:1966:ICA,
  author =       "D. S. Mitrinovi{\'c}",
  title =        "An inequality concerning the arithmetic and geometric
                 means",
  journal =      j-MATH-GAZ,
  volume =       "50",
  pages =        "310--311",
  year =         "1966",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.2307/3614693",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  MRclass =      "26.70",
  MRnumber =     "0229768",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}

@Article{Shisha:1966:GII,
  author =       "O. Shisha",
  title =        "Geometrical interpretations of the inequalities
                 between the arithmetic, geometric and harmonic means",
  journal =      j-MATH-MAG,
  volume =       "39",
  pages =        "268--269",
  year =         "1966",
  CODEN =        "MAMGA8",
  DOI =          "https://doi.org/10.2307/2689010",
  ISSN =         "0011-801x",
  MRclass =      "26.70",
  MRnumber =     "0202951",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Delta. University of Wisconsin",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}

@TechReport{Tricomi:1966:RUS,
  author =       "F. G. Tricomi",
  title =        "Lectures on the use of special functions by
                 calculations with electronic computers",
  type =         "Lecture Series",
  number =       "47",
  institution =  "The Institute for Fluid Dynamics and Applied
                 Mathematics, University of Maryland, College Park",
  address =      "College Park, MD, USA",
  year =         "1966",
  bibdate =      "Tue Mar 14 18:48:58 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bullen:1967:SMI,
  author =       "P. S. Bullen",
  title =        "Some more inequalities involving the arithmetic and
                 geometric means",
  journal =      "Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz.
                 No.",
  volume =       "181--196",
  pages =        "61--66",
  year =         "1967",
  ISSN =         "0522-8441",
  MRclass =      "26.70",
  MRnumber =     "0223515",
  MRreviewer =   "Z. Dar{\'o}czy",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Univerzitet u Beogradu. Publikacije Elektrotehni\v
                 ckog Fakulteta. Serija Matematika i Fizika",
}

@Article{Everitt:1967:LPA,
  author =       "W. N. Everitt",
  title =        "On a limit problem associated with the
                 arithmetic--geometric mean inequality",
  journal =      j-J-LOND-MATH-SOC,
  volume =       "42",
  pages =        "712--718",
  year =         "1967",
  CODEN =        "JLMSAK",
  DOI =          "https://doi.org/10.1112/jlms/s1-42.1.712",
  ISSN =         "0024-6107 (print), 1469-7750 (electronic)",
  ISSN-L =       "0024-6107",
  MRclass =      "26.70",
  MRnumber =     "0222229",
  MRreviewer =   "P. H. Diananda",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "See corrigendum \cite{Everitt:1969:CLP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the London Mathematical Society. Second
                 Series",
  journal-URL =  "http://jlms.oxfordjournals.org/content/by/year",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Gaines:1967:AMG,
  author =       "Fergus Gaines",
  title =        "Classroom Notes: On the Arithmetic Mean--Geometric
                 Mean Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "74",
  number =       "3",
  pages =        "305--306",
  month =        mar,
  year =         "1967",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2316036",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26.70 (15.00)",
  MRnumber =     "0214715",
  MRreviewer =   "A. Jaeger",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Klamkin:1968:ICA,
  author =       "Murray S. Klamkin",
  title =        "Inequalities concerning the arithmetic, geometric and
                 harmonic means",
  journal =      j-MATH-GAZ,
  volume =       "52",
  pages =        "156--157",
  year =         "1968",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.2307/3612687",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  MRclass =      "26.70",
  MRnumber =     "0229769",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}

@Article{Oppenheim:1968:ICA,
  author =       "A. Oppenheim",
  title =        "On inequalities connecting arithmetic means and
                 geometric means of two sets of three positive numbers.
                 {II}",
  journal =      "Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz.
                 No.",
  volume =       "210-228",
  pages =        "21--24",
  year =         "1968",
  ISSN =         "0522-8441",
  MRclass =      "26.70",
  MRnumber =     "0231960",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Univerzitet u Beogradu. Publikacije Elektrotehni\v
                 ckog Fakulteta. Serija Matematika i Fizika",
}

@Article{OShea:1968:MNA,
  author =       "Siobhan O'Shea",
  title =        "Mathematical Notes: The Arithmetic Geometric Mean
                 Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "75",
  number =       "10",
  pages =        "1092--1093",
  month =        dec,
  year =         "1968",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2315738",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "Contributed Item",
  MRnumber =     "1535171",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Book{Pars:1968:TAD,
  author =       "Leopold Alexander Pars",
  title =        "A Treatise on Analytical Dynamics",
  publisher =    "Heinemann",
  address =      "London, UK",
  pages =        "xxi + 641",
  year =         "1968",
  ISBN =         "0-435-52690-1",
  ISBN-13 =      "978-0-435-52690-0",
  bibdate =      "Wed Mar 15 08:09:52 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  remark =       "Reprint of \cite{Pars:1965:TAD} with corrections.",
}

@Article{Everitt:1969:CLP,
  author =       "W. N. Everitt",
  title =        "Corrigendum: {``On a limit problem associated with the
                 arithmetic--geometric mean inequality''}",
  journal =      j-J-LOND-MATH-SOC-2,
  volume =       "1",
  pages =        "428--430",
  year =         "1969",
  CODEN =        "JLMSAK",
  DOI =          "https://doi.org/10.1112/jlms/s2-1.1.428-s",
  ISSN =         "0024-6107 (print), 1469-7750 (electronic)",
  ISSN-L =       "0024-6107",
  MRclass =      "26.70",
  MRnumber =     "0248309",
  MRreviewer =   "P. H. Diananda",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "See \cite{Everitt:1967:LPA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the London Mathematical Society. Second
                 Series",
  journal-URL =  "http://jlms.oxfordjournals.org/content/by/year",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Carlson:1970:IMA,
  author =       "B. C. Carlson",
  title =        "An Inequality of Mixed Arithmetic and Geometric
                 Means",
  journal =      j-SIAM-REVIEW,
  volume =       "12",
  number =       "2",
  pages =        "287--288",
  month =        "????",
  year =         "1970",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1012054",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:06:17 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/12/2;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "April 1970",
}

@Article{Lehmer:1970:CM,
  author =       "D. H. Lehmer",
  title =        "On compounding of means",
  journal =      j-NAMS,
  volume =       "17",
  number =       "4",
  pages =        "634--635",
  month =        jun,
  year =         "1970",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibdate =      "Tue Mar 14 19:09:32 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lehmer-derrick-henry.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/nams1970.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Derrick Henry Lehmer (23 February 1905--22 May 1991)",
  ajournal =     "Notices Amer. Math. Soc.",
  fjournal =     "Notices of the American Mathematical Society",
  issue =        "122",
  journal-URL =  "http://www.ams.org/notices/",
}

@Article{Loewner:1970:DBG,
  author =       "Charles Loewner and Henry B. Mann",
  title =        "On the difference between the geometric and the
                 arithmetic mean of {$n$} quantities",
  journal =      j-ADV-MATH,
  volume =       "5",
  pages =        "472--473 (1970)",
  year =         "1970",
  CODEN =        "ADMTA4",
  DOI =          "https://doi.org/10.1016/0001-8708(70)90012-5",
  ISSN =         "0001-8708 (print), 1090-2082 (electronic)",
  ISSN-L =       "0001-8708",
  MRclass =      "26.70",
  MRnumber =     "0279259",
  MRreviewer =   "P. H. Diananda",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00018708",
}

@Article{Mitrovic:1970:SII,
  author =       "{\v{Z}}arko Mitrovi{\'c}",
  title =        "Some inequalities involving elementary symmetric
                 function and arithmetic and geometric means",
  journal =      j-MATH-GAZ,
  volume =       "54",
  pages =        "155--157",
  year =         "1970",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.2307/3612110",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  MRclass =      "26.70",
  MRnumber =     "0264010",
  MRreviewer =   "V. Ganapathy Iyer",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}

@Article{Carlson:1971:AIA,
  author =       "Bille Chandler Carlson",
  title =        "Algorithms Involving Arithmetic and Geometric Means",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "78",
  number =       "5",
  pages =        "496--505",
  month =        may,
  year =         "1971",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2317754",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "33.19",
  MRnumber =     "0283246",
  MRreviewer =   "F. G{\"o}tze",
  bibdate =      "Mon Jun 28 12:36:21 MDT 1999",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib; JSTOR
                 database",
  URL =          "http://www.jstor.org/stable/2317754",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Carlson:1971:MAG,
  author =       "B. C. Carlson and R. K. Meany and S. A. Nelson",
  title =        "Mixed arithmetic and geometric means",
  journal =      j-PAC-J-MATH,
  volume =       "38",
  pages =        "343--349",
  year =         "1971",
  CODEN =        "PJMAAI",
  ISSN =         "0030-8730 (print), 1945-5844 (electronic)",
  ISSN-L =       "0030-8730",
  MRclass =      "26A87",
  MRnumber =     "0304590",
  MRreviewer =   "H. Kober",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://projecteuclid.org/euclid.pjm/1102970046",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Mathematics",
  journal-URL =  "http://msp.org/pjm",
}

@Article{Lehmer:1971:CCM,
  author =       "D. H. Lehmer",
  title =        "On the compounding of certain means",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "36",
  number =       "1",
  pages =        "183--200",
  month =        oct,
  year =         "1971",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/0022-247X(71)90029-1",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "10.43",
  MRnumber =     "281696",
  MRreviewer =   "D. Rearick",
  bibdate =      "Tue Mar 14 18:52:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lehmer-derrick-henry.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/0022247X71900291",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "arithmetic--geometric mean (AGM) iteration; complete
                 elliptic integrals of the first and second kinds.
                 Landen s transformation",
}

@Article{Meany:1971:BRB,
  author =       "R. K. Meany and S. A. Nelson and B. C. Carlson",
  title =        "Book Review: {{\booktitle{An Inequality of Mixed
                 Arithmetic and Geometric Means}} (B. C. Carlson)}",
  journal =      j-SIAM-REVIEW,
  volume =       "13",
  number =       "2",
  pages =        "253--255",
  month =        "????",
  year =         "1971",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1013058",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:06:28 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/13/2;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "April 1971",
}

@Article{Morita:1971:CLG,
  author =       "Tohru Morita and Tsuyoshi Horiguchi",
  title =        "Calculation of the lattice {Green}'s function for the
                 bcc, fcc, and rectangular lattices",
  journal =      j-J-MATH-PHYS,
  volume =       "12",
  number =       "6",
  pages =        "986--992",
  month =        jun,
  year =         "1971",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1665693",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 16:39:38 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v12/i6/p986_s1",
  acknowledgement = ack-nhfb,
  classification = "A0550 (Lattice theory and statistics; Ising
                 problems)",
  corpsource =   "Tohoku Univ., Sendai, Japan",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "arithmetic mean; bcc lattice; complex modulus;
                 divergence; elliptic integral; fcc lattice; geometric
                 mean; Green's function methods; Lattice Green function;
                 lattice theory and statistics; rectangular lattice",
  onlinedate =   "28 October 2003",
  pagecount =    "7",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Passy:1971:GWM,
  author =       "U. Passy",
  title =        "Generalized Weighted Mean Programming",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "20",
  number =       "4",
  pages =        "763--778",
  month =        jun,
  year =         "1971",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classification = "B0260 (Optimisation techniques); C1180 (Optimisation
                 techniques)",
  corpsource =   "Tech. Israel Inst. Technol., Haifa, Israel",
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  keywords =     "algorithms; arithmetic geometric mean inequality;
                 nonlinear programming; weighted mean programming",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Hering:1972:GAG,
  author =       "Franz Hering",
  title =        "A generalization of the arithmetic--geometric mean
                 inequality and an application to finite sequences of
                 zeros and ones",
  journal =      j-ISRAEL-J-MATH,
  volume =       "11",
  number =       "1",
  pages =        "14--30",
  year =         "1972",
  CODEN =        "ISJMAP",
  DOI =          "https://doi.org/10.1007/BF02761445",
  ISSN =         "0021-2172 (print), 1565-8511 (electronic)",
  ISSN-L =       "0021-2172",
  MRclass =      "05A17",
  MRnumber =     "0302466",
  MRreviewer =   "S. G. Williamson",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02761445",
  acknowledgement = ack-nhfb,
  fjournal =     "Israel Journal of Mathematics",
  journal-URL =  "http://link.springer.com/journal/11856",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Morita:1972:CAG,
  author =       "Tohru Morita and Tsuyoshi Horiguchi",
  title =        "Convergence of the arithmetic--geometric mean
                 procedure for the complex variables and the calculation
                 of the complete elliptic integrals with complex
                 modulus",
  journal =      j-NUM-MATH,
  volume =       "20",
  number =       "5",
  pages =        "425--430",
  month =        oct,
  year =         "1972",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01402565",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D20",
  MRnumber =     "0315870",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=20&issue=5&spage=425",
  abstract =     "The convergence of the arithmetic--geometric mean
                 procedure is checked for complex variables. The
                 procedure is shown to be useful for the evaluation of
                 the complete elliptic integrals of the first and second
                 kinds with complex modulus. It is suggested that the
                 procedure will be useful also for the numerical
                 calculation of the elliptic integrals and the Jacobian
                 elliptic functions with complex modulus in general.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Thurston:1972:HGU,
  author =       "H. A. Thurston",
  title =        "How good is the usual approximation for the period of
                 a simple pendulum?",
  journal =      j-MATH-GAZ,
  volume =       "56",
  number =       "??",
  pages =        "120--122",
  month =        "????",
  year =         "1972",
  CODEN =        "MAGAAS",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  bibdate =      "Wed Mar 15 07:24:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  keywords =     "arithmetic--geometric mean",
}

@Article{Vasic:1972:ICA,
  author =       "Petar M. Vasi{\'c}",
  title =        "On inequalities connecting arithmetic means and
                 geometric means of two sets of $n$ positive numbers",
  journal =      "Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat.
                 Fiz.",
  volume =       "381--409",
  pages =        "63--66",
  year =         "1972",
  ISSN =         "0522-8441",
  MRclass =      "26A86",
  MRnumber =     "0333098",
  MRreviewer =   "Victor I. Levin",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Univerzitet u Beogradu. Publikacije Elektrotehni\v
                 ckog Fakulteta. Serija Matematika i Fizika",
}

@TechReport{Brent:1975:FMP,
  author =       "R. P. Brent",
  title =        "Fast Multiple-precision Evaluation of Elementary
                 Functions",
  type =         "Technical Report",
  number =       "STAN-CS-75-515",
  institution =  inst-STAN-CS,
  address =      inst-STAN-CS:adr,
  pages =        "i + 22",
  month =        aug,
  year =         "1975",
  bibdate =      "Thu Jan 11 16:47:21 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://bitsavers.org/pdf/stanford/cs_techReports/STAN-CS-75_515_Brent_Fast_Multiple-Precision_Evaluation_Of_Elementary_Functions_Aug75.pdf",
  abstract =     "Let $ f(x) $ be one of the usual elementary functions
                 ($ \exp $, $ \log $, $ \arctan $, $ \sin $, $ \cosh $,
                 etc.), and let $ M(n) $ be the number of
                 single-precision operations required to multiply n-bit
                 integers. We show that f(x) can be evaluated, with
                 relative error $ O(2^{-n}) $, in $ O(M(n) \log (n)) $
                 operations as $ n \to \infty $, for any floating-point
                 number $x$ (with an $n$-bit fraction) in a suitable
                 finite interval. From the Sch{\"o}nhage--Strassen bound
                 on $ M(n)$, it follows that an $n$-bit approximation to
                 $ f(x)$ may be evaluated in $ O(n \log^2 (n) \log \log
                 (n))$ operations. Special cases include the evaluation
                 of constants such as $ \pi $, $e$, and $ e^p i$. The
                 algorithms depend on the theory of elliptic integrals,
                 using the arithmetic--geometric mean iteration and
                 ascending Landen transformations.",
  acknowledgement = ack-nhfb,
}

@Article{Tung:1975:LUB,
  author =       "S. H. Tung",
  title =        "On lower and upper bounds of the difference between
                 the arithmetic and the geometric mean",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "131",
  pages =        "834--836",
  month =        jul,
  year =         "1975",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2005294",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "26A87",
  MRnumber =     "0393393",
  MRreviewer =   "D. C. Benson",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0240 (Probability and statistics); C1140 (Probability
                 and statistics)",
  corpsource =   "Dept. of Math. and Statistics, Miami Univ., Oxford,
                 OH, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "arithmetic mean; geometric mean; lower bounds;
                 statistics; upper bounds",
  treatment =    "T Theoretical or Mathematical",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Brent:1976:FMP,
  author =       "Richard P. Brent",
  title =        "Fast Multiple-Precision Evaluation of Elementary
                 Functions",
  journal =      j-J-ACM,
  volume =       "23",
  number =       "2",
  pages =        "242--251",
  month =        apr,
  year =         "1976",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321941.321944",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "68A20 (68A10)",
  MRnumber =     "52 \#16111",
  MRreviewer =   "Amnon Barak",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  abstract =     "Let $ f(x) $ be one of the usual elementary functions
                 ($ \exp $, $ \log $, $ \arctan $, $ \sin $, $ \cosh $,
                 etc.), and let $ M(n) $ be the number of
                 single-precision operations required to multiply
                 $n$-bit integers. It is shown that $ f(x) $ can be
                 evaluated, with relative error $ O(2 - n) $, in $
                 O(M(n)l o g (n)) $ operations as $ n \rightarrow \infty
                 $, for any floating-point number $x$ (with an $n$-bit
                 fraction) in a suitable finite interval. From the
                 Sch{\"o}nhage--Strassen bound on $ M(n) $, it follows
                 that an $n$-bit approximation to $ f(x) $ may be
                 evaluated in $ O(n \log_(n) \log \log (n)) $
                 operations. Special cases include the evaluation of
                 constants such as $ \pi^e$, and $ e^\pi $. The
                 algorithms depend on the theory of elliptic integrals,
                 using the arithmetic--geometric mean iteration and
                 ascending Landen transformations.",
  acknowledgement = ack-nhfb,
  classification = "723",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  journalabr =   "J Assoc Comput Mach",
  keywords =     "computational complexity; computer arithmetic;
                 computer programming",
}

@InProceedings{Brent:1976:MPZ,
  author =       "Richard P. Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  crossref =     "Traub:1976:ACC",
  pages =        "151--176",
  year =         "1976",
  MRclass =      "68A20",
  MRnumber =     "54 \#11843",
  MRreviewer =   "Claus-Peter Schnorr",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Chong:1976:AMG,
  author =       "Kong Ming Chong",
  title =        "The arithmetic mean-geometric mean inequality: a new
                 proof",
  journal =      j-MATH-MAG,
  volume =       "49",
  number =       "2",
  pages =        "87--88",
  year =         "1976",
  CODEN =        "MAMGA8",
  DOI =          "https://doi.org/10.2307/2689438",
  ISSN =         "0011-801x",
  MRclass =      "26A86",
  MRnumber =     "0399388",
  MRreviewer =   "Peter Bullen",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Delta. University of Wisconsin",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}

@Article{Fink:1976:GAG,
  author =       "A. M. Fink and Max {Jodeit, Jr.}",
  title =        "A generalization of the arithmetic--geometric means
                 inequality",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "61",
  number =       "2",
  pages =        "255--261 (1977)",
  year =         "1976",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.2307/2041321",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "26A86",
  MRnumber =     "0427564",
  MRreviewer =   "E. F. Beckenbach",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Glaser:1976:RGM,
  author =       "Ronald E. Glaser",
  title =        "The ratio of the geometric mean to the arithmetic mean
                 for a random sample from a gamma distribution",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "71",
  number =       "354",
  pages =        "480--487",
  year =         "1976",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274x (electronic)",
  ISSN-L =       "0162-1459",
  MRclass =      "62E15",
  MRnumber =     "0403011",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://links.jstor.org/sici?sici=0162-1459(197606)71:354<480:TROTGM>2.0.CO;2-I&origin=MSN",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Salamin:1976:CUA,
  author =       "Eugene Salamin",
  title =        "Computation of $ \pi $ Using Arithmetic--Geometric
                 Mean",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "135",
  pages =        "565--570",
  month =        jul,
  year =         "1976",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2005327",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "10A30 (10A40 33A25)",
  MRnumber =     "0404124 (53 \#7928)",
  MRreviewer =   "I. John Zucker",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib; JSTOR
                 database; MathSciNet database",
  note =         "See also \cite{Brent:1976:MPZ,Brent:2010:MPZ}.",
  URL =          "http://www.jstor.org/stable/2005327",
  ZMnumber =     "0345.10003",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Charles Stark Draper Lab., Cambridge, MA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "arithmetic geometric mean; convergence; elliptic
                 integrals; error analysis; fast Fourier transform
                 multiplication; function evaluation; Landen's;
                 Legendre's relation; numerical computation of pi;
                 transformation",
  remark =       "Fullerton: A quadratically convergent algorithm.",
  treatment =    "A Application; T Theoretical or Mathematical",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Chong:1977:AMG,
  author =       "Kong Ming Chong",
  title =        "On the arithmetic-mean-geometric-mean inequality",
  journal =      "Nanta Math.",
  volume =       "10",
  number =       "1",
  pages =        "26--27",
  year =         "1977",
  ISSN =         "0077-2739",
  MRclass =      "26A86",
  MRnumber =     "0460568",
  MRreviewer =   "G. Sansone",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Nanyang University. Nanta Mathematica",
}

@Article{Schaumberger:1977:APA,
  author =       "Norman Schaumberger and Bert Kabak",
  title =        "Another proof of the arithmetic--geometric mean
                 inequality",
  journal =      j-PI-MU-EPSILON-J,
  volume =       "6",
  number =       "6",
  pages =        "352--354",
  year =         "1977",
  CODEN =        "PMEJBR",
  ISSN =         "0031-952x",
  MRclass =      "26A86",
  MRnumber =     "0430190",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Pi Mu Epsilon Journal",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Almkvist:1978:AGM,
  author =       "Gert Almkvist",
  title =        "Aritmetisk--geometriska Medelv{\"a}rdet och Ellipsens
                 B{\aa}gl{\"a}ngd. ({Swedish}) [{The}
                 arithmetic--geometric mean and the arc length of the
                 ellipse]",
  journal =      j-NORDISK-MATH-TIDSKR,
  volume =       "25--26",
  number =       "3--4",
  pages =        "121--130, 208",
  year =         "1978",
  ISSN =         "0029-1412, 0801-3500",
  MRclass =      "10D05 (33A25)",
  MRnumber =     "561786",
  MRreviewer =   "Troels J{\o}rgensen",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/24525291",
  acknowledgement = ack-nhfb,
  fjournal =     "Nordisk Matematisk Tidskrift",
  journal-URL =  "http://www.jstor.org/journal/nordmatetids",
  language =     "Swedish",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Bajpai:1978:SAG,
  author =       "S. K. Bajpai",
  title =        "Special arithmetic and geometric means preserve {$
                 \Phi $}-like univalence",
  journal =      "Rev. Colombiana Mat.",
  volume =       "12",
  number =       "3-4",
  pages =        "83--90",
  year =         "1978",
  ISSN =         "0034-7426",
  MRclass =      "30C45",
  MRnumber =     "533713",
  MRreviewer =   "P. T. Mocanu",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Revista Colombiana de Matem{\'a}ticas",
}

@Article{Cartwright:1978:RAM,
  author =       "D. I. Cartwright and M. J. Field",
  title =        "A refinement of the arithmetic mean-geometric mean
                 inequality",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "71",
  number =       "1",
  pages =        "36--38",
  year =         "1978",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.2307/2042211",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "26A87",
  MRnumber =     "0476971",
  MRreviewer =   "V. Ganapathy Iyer",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@Article{Landsberg:1978:TPI,
  author =       "P. T. Landsberg",
  title =        "A thermodynamic proof of the inequality between
                 arithmetic and geometric mean",
  journal =      j-PHYS-LET-A,
  volume =       "67",
  number =       "1",
  pages =        "1",
  year =         "1978",
  CODEN =        "PYLAAG",
  DOI =          "https://doi.org/10.1016/0375-9601(78)90548-0",
  ISSN =         "0031-9163 (print), 1873-2410 (electronic)",
  ISSN-L =       "0375-9601",
  MRclass =      "80A10 (26D20)",
  MRnumber =     "601317",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Letters. A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03759601",
}

@Article{Schaumberger:1978:CPA,
  author =       "Norman Schaumberger",
  title =        "A Calculus Proof of the Arithmetic-Geometric Mean
                 Inequality",
  journal =      j-TWO-YEAR-COLL-MATH-J,
  volume =       "9",
  number =       "1",
  pages =        "16--17",
  month =        jan,
  year =         "1978",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/00494925.1978.11974538",
  ISSN =         "0049-4925 (print), 2325-9116 (electronic)",
  ISSN-L =       "0049-4925",
  bibdate =      "Thu Feb 14 09:48:43 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/00494925.1978.11974538",
  acknowledgement = ack-nhfb,
  fjournal =     "Two-Year College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 http://www.jstor.org/journals/00494925.html",
  onlinedate =   "30 Jan 2018",
}

@Article{Abriata:1979:CTP,
  author =       "J. P. Abriata",
  title =        "Comment on a thermodynamic proof of the inequality
                 between arithmetic and geometric mean",
  journal =      j-PHYS-LET-A,
  volume =       "71",
  number =       "4",
  pages =        "309--310",
  year =         "1979",
  CODEN =        "PYLAAG",
  DOI =          "https://doi.org/10.1016/0375-9601(79)90061-6",
  ISSN =         "0031-9163 (print), 1873-2410 (electronic)",
  ISSN-L =       "0375-9601",
  MRclass =      "80A10 (26D20)",
  MRnumber =     "588726",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Letters. A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03759601",
}

@InCollection{Krafft:1979:RGA,
  author =       "Olaf Krafft and Rudolf Mathar and Martin Schaefer",
  booktitle =    "Numerische {Methoden} bei graphentheoretischen und
                 kombinatorischen {Problemen}, {Band} 2 ({Tagung},
                 {Math}. {Forschungsinst}., {Oberwolfach}, 1978)",
  title =        "A refined geometric--arithmetic means inequality for
                 integers",
  volume =       "46",
  publisher =    "Birkh{\"a}user, Basel-Boston, Mass.",
  pages =        "216--223",
  year =         "1979",
  MRclass =      "26D20 (10E99)",
  MRnumber =     "562279",
  MRreviewer =   "Norbert Schmitz",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "Internat. Ser. Numer. Math.",
  acknowledgement = ack-nhfb,
}

@Book{Pars:1979:TAD,
  author =       "Leopold Alexander Pars",
  title =        "A Treatise on Analytical Dynamics",
  publisher =    "Ox Bow Press",
  address =      "Woodbridge, CT, USA",
  pages =        "xxi + 641",
  year =         "1979",
  ISBN =         "0-918024-07-2",
  ISBN-13 =      "978-0-918024-07-7",
  LCCN =         "QA845 .P32 1979",
  bibdate =      "Wed Mar 15 08:12:22 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Reprint. Originally published: New York: Wiley,
                 1965.",
  subject =      "Dynamics",
  tableofcontents = "Motion of a particle \\
                 Dynamical Systems \\
                 The first form of the fundamental equation \\
                 The second and third forms of the fundamental equation
                 \\
                 Lagrangian coordinates \\
                 Lagrange's equations \\
                 The theory of rotations \\
                 First applications of Lagrange's equations \\
                 The theory of vibrations \\
                 Further applications of Lagrange's equations \\
                 Variable mass \\
                 The Gibbs--Appell equations \\
                 Applications of the Gibbs--Appell equations \\
                 Impulsive motion \\
                 The sixth form of the fundamental equation \\
                 The Hamilton--Jacobi theorem \\
                 Separable systems with n degrees of freedom \\
                 Systems with one degree of freedom, motion near a
                 singular point \\
                 Systems with one degree of freedom, the cyclic
                 characteristics \\
                 Systems with n degrees of freedom, properties of the
                 characteristics \\
                 Hamilton's equations \\
                 Motion in the neighborhood of a given motion, stability
                 in motion \\
                 Contact transformations \\
                 Transformation theory \\
                 Variation principles \\
                 The principle of Least Action \\
                 The restricted problem of three bodies \\
                 The problem of three bodies \\
                 Periodic orbits",
}

@Article{Nandi:1980:EDN,
  author =       "S. B. Nandi",
  title =        "On the exact distribution of a normalized ratio of the
                 weighted geometric mean to the unweighted arithmetic
                 mean in samples from gamma distributions",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "75",
  number =       "369",
  pages =        "217--220",
  year =         "1980",
  CODEN =        "JSTNAL",
  ISSN =         "0003-1291",
  ISSN-L =       "0162-1459",
  MRclass =      "62E15 (62F05)",
  MRnumber =     "568595",
  MRreviewer =   "G. S. Lingappaiah",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://links.jstor.org/sici?sici=0162-1459(198003)75:369<217:OTEDOA>2.0.CO;2-M&origin=MSN",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Cusmariu:1981:MNP,
  author =       "Adolf Cusmariu",
  title =        "Mathematical Notes: a Proof of the Arithmetic
                 Mean--Geometric Mean Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "88",
  number =       "3",
  pages =        "192--194",
  month =        mar,
  year =         "1981",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2320467",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26D15 (05A20 40A99)",
  MRnumber =     "619566 (82g:26024)",
  MRreviewer =   "D. C. Russell",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Fink:1981:WAG,
  author =       "A. M. Fink",
  title =        "A weighted-arithmetic--geometric means inequality",
  journal =      "Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat.
                 Fiz.",
  volume =       "716--734",
  number =       "716-734",
  pages =        "35--40",
  year =         "1981",
  ISSN =         "0522-8441",
  MRclass =      "26D15",
  MRnumber =     "642007",
  MRreviewer =   "Peter Bullen",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Univerzitet u Beogradu. Publikacije Elektrotehni\v
                 ckog Fakulteta. Serija Matematika i Fizika",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Heinrich:1981:VAG,
  author =       "H. Heinrich",
  title =        "{Eine Verallgemeinerung des
                 arithmetisch--geometrischen Mittels}. ({German}) [{A}
                 generalization of the arithmetic--geometric mean]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "61",
  number =       "6",
  pages =        "265--267",
  year =         "1981",
  CODEN =        "ZAMMAX",
  DOI =          "https://doi.org/10.1002/zamm.19810610610",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  MRclass =      "26D15",
  MRnumber =     "638023",
  MRreviewer =   "E. F. Beckenbach",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik. Ingenieurwissenschaftliche
                 Forschungsarbeiten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
  language =     "German",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Perisastry:1982:BRA,
  author =       "M. Perisastry and V. N. Murty",
  title =        "Bounds for the Ratio of the Arithmetic Mean to the
                 Geometric Mean",
  journal =      j-TWO-YEAR-COLL-MATH-J,
  volume =       "13",
  number =       "2",
  pages =        "160--161",
  month =        mar,
  year =         "1982",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/00494925.1982.11972600",
  ISSN =         "0049-4925 (print), 2325-9116 (electronic)",
  ISSN-L =       "0049-4925",
  bibdate =      "Thu Feb 14 09:49:31 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/00494925.1982.11972600",
  acknowledgement = ack-nhfb,
  fjournal =     "Two-Year College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 http://www.jstor.org/journals/00494925.html",
  onlinedate =   "30 Jan 2018",
}

@Article{Schaumberger:1982:SAP,
  author =       "Norman Schaumberger",
  title =        "Still Another Proof of the Arithmetic-Geometric Mean
                 Inequality",
  journal =      j-TWO-YEAR-COLL-MATH-J,
  volume =       "13",
  number =       "2",
  pages =        "159--160",
  month =        mar,
  year =         "1982",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/00494925.1982.11972599",
  ISSN =         "0049-4925 (print), 2325-9116 (electronic)",
  ISSN-L =       "0049-4925",
  bibdate =      "Thu Feb 14 09:49:31 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/00494925.1982.11972599",
  acknowledgement = ack-nhfb,
  fjournal =     "Two-Year College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 http://www.jstor.org/journals/00494925.html",
  onlinedate =   "30 Jan 2018",
}

@Article{Ando:1983:AGH,
  author =       "T. Ando",
  title =        "On the arithmetic--geometric-harmonic-mean
                 inequalities for positive definite matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "52/53",
  pages =        "31--37",
  year =         "1983",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/0024-3795(83)80005-6",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A45 (15A48 47A60)",
  MRnumber =     "709342",
  MRreviewer =   "George P. Barker",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Borwein:1983:GAG,
  author =       "D. Borwein and P. B. Borwein",
  title =        "A Generalized Arithmetic--Geometric Mean",
  journal =      j-SIAM-REVIEW,
  volume =       "25",
  number =       "3",
  pages =        "401--401",
  month =        "????",
  year =         "1983",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1025081",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:53:39 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/25/3;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "July 1983",
}

@Article{Ono:1983:GGT,
  author =       "Takashi Ono",
  title =        "A generalization of {Gauss}' theorem on
                 arithmetic--geometric means",
  journal =      j-PROC-JAPAN-ACAD-SER-A-MATH-SCI,
  volume =       "59",
  number =       "4",
  pages =        "154--157",
  year =         "1983",
  CODEN =        "PJAADT",
  ISSN =         "0386-2194",
  MRclass =      "33A30 (30D10)",
  MRnumber =     "711323",
  MRreviewer =   "R. A. Askey",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://projecteuclid.org/euclid.pja/1195515639",
  acknowledgement = ack-nhfb,
  fjournal =     "Japan Academy. Proceedings. Series A. Mathematical
                 Sciences",
  journal-URL =  "http://projecteuclid.org/pja",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Borwein:1984:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "26",
  number =       "3",
  pages =        "351--366",
  month =        jul,
  year =         "1984",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1026073",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65D20 (26A09)",
  MRnumber =     "750454; 86d:65029",
  MRreviewer =   "S. Conde",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://epubs.siam.org/toc/siread/26/3;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://www.jstor.org/stable/2031275",
  abstract =     "We produce a self contained account of the
                 relationship between the Gaussian arithmetic--geometric
                 mean iteration and the fast computation of elementary
                 functions. A particularly pleasant algorithm for pi is
                 one of the by-products.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliationaddress = "Dalhousie Univ, Halifax, NS, Can",
  classification = "723; 921",
  fjournal =     "SIAM Review. A Publication of the Society for
                 Industrial and Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "AGM (Arithmetic--Geometric Mean);
                 arithmetic--geometric mean; calculation of pi;
                 computational methods; elliptic functions; Iterative
                 Methods; mathematical techniques; numerical
                 mathematics",
  onlinedate =   "July 1984",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Borwein:1984:GAG,
  author =       "D. Borwein and P. B. Borwein",
  title =        "A Generalized Arithmetic--Geometric Mean",
  journal =      j-SIAM-REVIEW,
  volume =       "26",
  number =       "3",
  pages =        "433--433",
  month =        jul,
  year =         "1984",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1026085",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:53:48 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/26/3;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  keywords =     "AGM (Arithmetic--Geometric Mean)",
  onlinedate =   "July 1984",
}

@TechReport{Borwein:1984:RCC,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "Reduced Complexity Calculation of Log",
  number =       "DALTR 84-01",
  institution =  "Department of Mathematics, Dalhousie University",
  address =      "Halifax, NS, Canada",
  pages =        "17",
  month =        jan,
  year =         "1984",
  bibdate =      "Mon Nov 07 17:37:11 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  abstract =     "Various reduced complexity methods for high precision
                 computation of the logarithm are investigated.",
  acknowledgement = ack-nhfb,
  keywords =     "analytic complexity; arithmetic--geometric mean;
                 binary splitting; bit complexity; elliptic integrals;
                 Fast Fourier Transform; logarithms; operational
                 complexity; theta functions",
  remark =       "Typescript, with 84-01 added by hand on cover page.",
}

@Article{Cox:1984:AGM,
  author =       "David A. Cox",
  title =        "The arithmetic--geometric mean of {Gauss}",
  journal =      j-ENSEIGN-MATH-2,
  volume =       "30",
  number =       "3--4",
  pages =        "275--330",
  year =         "1984",
  CODEN =        "ENMAAR",
  ISSN =         "0013-8584 (print), 2309-4672 (electronic)",
  MRclass =      "01A55 (11B83 11F03 14K25)",
  MRnumber =     "767905",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "L'Enseignement Math{\'e}matique. Revue Internationale.
                 2e S{\'e}rie",
  journal-URL =  "http://www.e-periodica.ch/digbib/vollist?var=true&UID=ens-001",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Foster:1984:AHM,
  author =       "D. M. E. Foster and G. M. Phillips",
  title =        "The Arithmetic--Harmonic Mean",
  journal =      j-MATH-COMPUT,
  volume =       "42",
  number =       "165",
  pages =        "183--191",
  month =        jan,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "40A99 (40A25)",
  MRnumber =     "85j:40008",
  MRreviewer =   "Amnon Jakimovski",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1120 (Mathematical analysis)",
  corpsource =   "Maths. Inst., Univ. of St. Andrews, St. Andrews, Fife,
                 UK",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Archimedean process; arithmetic--harmonic; geometric
                 mean; harmonic analysis; harmonic means; mean;
                 sequences",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Schoen:1984:HGA,
  author =       "Robert Schoen",
  title =        "Harmonic, Geometric, and Arithmetic Means in
                 Generalized {Fibonacci} Sequences",
  journal =      j-FIB-QUART,
  volume =       "22",
  number =       "4",
  pages =        "354--357",
  month =        nov,
  year =         "1984",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  MRclass =      "11B39",
  MRnumber =     "766313",
  bibdate =      "Thu Oct 20 18:00:35 MDT 2011",
  bibsource =    "http://www.fq.math.ca/22-4.html;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/22-4/schoen.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Cox:1985:GAG,
  author =       "David A. Cox",
  title =        "{Gauss} and the arithmetic--geometric mean",
  journal =      j-NAMS,
  volume =       "32",
  number =       "2",
  pages =        "147--151",
  year =         "1985",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  MRclass =      "01A55 (11-03 14-03)",
  MRnumber =     "779224",
  MRreviewer =   "Willard Parker",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Eddy:1985:BAG,
  author =       "Roland H. Eddy",
  title =        "Behold! {The} {Arithmetic-Geometric Mean Inequality}",
  journal =      j-COLLEGE-MATH-J,
  volume =       "16",
  number =       "3",
  pages =        "208--208",
  month =        jun,
  year =         "1985",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.1985.11972881",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:50:09 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/07468342.1985.11972881",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  onlinedate =   "30 Jan 2018",
}

@Article{Newman:1985:SVF,
  author =       "D. J. Newman",
  title =        "A simplified version of the fast algorithms of {Brent}
                 and {Salamin}",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "169",
  pages =        "207--210",
  month =        jan,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "86e:65030",
  MRreviewer =   "Walter Gautschi",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "exponential; fast algorithms; function approximation;
                 function approximations; Gauss arithmetic--geometric
                 process; pi",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Borwein:1986:MQC,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "More quadratically converging algorithms for $ \pi $",
  journal =      j-MATH-COMPUT,
  volume =       "46",
  number =       "173",
  pages =        "247--253",
  month =        jan,
  year =         "1986",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2008229",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "815846; 87e:65014",
  MRreviewer =   "M. M. Chawla",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib; JSTOR
                 database",
  URL =          "http://docserver.carma.newcastle.edu.au/1614/",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 B0290Z (Other numerical methods); C4130 (Interpolation
                 and function approximation); C4190 (Other numerical
                 methods)",
  corpsource =   "Dalhousie Univ., Halifax, NS, Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "arithmetic--geometric mean iteration; complete
                 elliptic; convergence of numerical methods;
                 Gauss--Legendre iteration; geometry; integrals;
                 iterative; Legendre formula; methods; pi evaluation;
                 quadratically converging algorithms",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Huda:1986:ESE,
  author =       "S. Huda and Rahul Mukerjee",
  title =        "{Edgeworth} series expansion for the distribution of
                 the log of the ratio of arithmetic mean to geometric
                 mean",
  journal =      "Pakistan J. Statist.",
  volume =       "2",
  number =       "2",
  pages =        "69--72",
  year =         "1986",
  MRclass =      "62E20",
  MRnumber =     "909876",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Pakistan Journal of Statistics",
}

@Article{Razpet:1986:MAG,
  author =       "Marko Razpet",
  title =        "A method of arithmetic--geometric mean",
  journal =      j-OBZORNIK-MAT-FIZ,
  volume =       "33",
  number =       "6",
  pages =        "161--164",
  year =         "1986",
  CODEN =        "OBMFAY",
  ISSN =         "0473-7446",
  MRclass =      "65D30 (65D32)",
  MRnumber =     "856885",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dru{\v{s}}tvo Matematikov, Fizikov in Astronomov SRS.
                 Obzornik za Matematiko in Fiziko",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Schattschneider:1986:PWA,
  author =       "Doris Schattschneider",
  title =        "Proof without Words: The Arithmetic Mean--Geometric
                 Mean Inequality",
  journal =      j-MATH-MAG,
  volume =       "59",
  number =       "1",
  pages =        "11",
  year =         "1986",
  CODEN =        "MAMGA8",
  ISSN =         "0025-570X",
  MRnumber =     "1572599",
  bibdate =      "Tue Aug 15 11:19:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/2690011?origin=pubexport",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}

@Article{Zulauf:1986:SFE,
  author =       "A. Zulauf",
  title =        "Solution of a functional equation by use of weighted
                 arithmetic--geometric means",
  journal =      j-INDIAN-J-MATH,
  volume =       "28",
  number =       "1",
  pages =        "49--56",
  year =         "1986",
  CODEN =        "IJOMAL",
  ISSN =         "0019-5324",
  MRclass =      "39B40",
  MRnumber =     "868947",
  MRreviewer =   "F. W. Carroll",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Indian Journal of Mathematics",
  journal-URL =  "http://www.amsallahabad.org/ijm.html",
  zzbibdate =    "Tue Aug 15 11:19:53 2017",
}

@Article{Alzer:1987:UZG,
  author =       "Horst Alzer",
  title =        "{{\"U}ber die Ungleichung zwischen dem geometrischen
                 und dem arithmetischen Mittel}. ({German}) [{On} the
                 inequality between the geometric and the arithmetic
                 mean]",
  journal =      "Quaestiones Math.",
  volume =       "10",
  number =       "4",
  pages =        "351--356",
  year =         "1987",
  ISSN =         "0379-9468",
  MRclass =      "26D15",
  MRnumber =     "908677",
  MRreviewer =   "L. Losonczi",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Quaestiones Mathematicae",
  language =     "German",
}

@Unpublished{Borwein:1987:AGM,
  author =       "Jonathan M. Borwein",
  title =        "The arithmetic--geometric mean of {Gauss} and
                 {Legendre}: An Excursion",
  day =          "15",
  month =        dec,
  year =         "1987",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Canadian Mathematical Society, Coxeter--James Lecture,
                 Vancouver, BC, Canada.",
  acknowledgement = ack-nhfb,
}

@Book{Borwein:1987:PAS,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "Pi and the {AGM}: a Study in Analytic Number Theory
                 and Computational Complexity",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xv + 414",
  year =         "1987",
  ISBN =         "0-471-83138-7, 0-471-31515-X (paperback)",
  ISBN-13 =      "978-0-471-83138-9, 978-0-471-31515-5 (paperback)",
  LCCN =         "QA241 .B774 1987",
  MRclass =      "11Y60 (68Q30)",
  MRnumber =     "877728",
  MRreviewer =   "H. London",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Canadian Mathematical Society series of monographs and
                 advanced texts = Monographies et {\'e}tudes de la
                 Soci{\'e}t{\'e} math{\'e}matique du Canada",
  acknowledgement = ack-nhfb,
  remark =       "Chinese edition 1995.",
  subject =      "Number theory; Computational complexity; Elliptic
                 functions; Pi",
  xxURL =        "http://www.loc.gov/catdir/description/wiley032/86015811.html;
                 http://www.loc.gov/catdir/toc/onix02/86015811.html",
}

@Article{Burk:1987:NGL,
  author =       "Frank Burk",
  title =        "Notes: The Geometric, Logarithmic, and Arithmetic Mean
                 Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "94",
  number =       "6",
  pages =        "527--528",
  month =        jun # "\slash " # jul,
  year =         "1987",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2322844",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "DML",
  MRnumber =     "1541119",
  bibdate =      "Mon Jun 28 12:38:44 MDT 1999",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Cohen:1987:AGM,
  author =       "Joel E. Cohen and Roger D. Nussbaum",
  title =        "Arithmetic--geometric means of positive matrices",
  journal =      j-MATH-PROC-CAMB-PHILOS-SOC,
  volume =       "101",
  number =       "2",
  pages =        "209--219",
  year =         "1987",
  CODEN =        "MPCPCO",
  DOI =          "https://doi.org/10.1017/S0305004100066561",
  ISSN =         "0305-0041 (print), 1469-8064 (electronic)",
  ISSN-L =       "0305-0041",
  MRclass =      "15A51",
  MRnumber =     "870592",
  MRreviewer =   "Ray C. Shiflett",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Proceedings of the Cambridge
                 Philosophical Society",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PSP",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Minassian:1987:NAG,
  author =       "Donald P. Minassian",
  title =        "Notes: The Arithmetic--Geometric Mean Inequality
                 Revisited: Elementary Calculus and Negative Numbers",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "94",
  number =       "10",
  pages =        "977--978",
  month =        dec,
  year =         "1987",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2322605",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26D15",
  MRnumber =     "936057 (89e:26035)",
  MRreviewer =   "G. A. Heuer",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Nelsen:1987:PWH,
  author =       "Roger B. Nelsen",
  title =        "Proof without Words: The Harmonic Mean--Geometric
                 Mean--Arithmetic Mean--Root Mean Square Ineqality",
  journal =      j-MATH-MAG,
  volume =       "60",
  number =       "3",
  pages =        "158",
  year =         "1987",
  CODEN =        "MAMGA8",
  ISSN =         "0025-570X",
  MRclass =      "DML",
  MRnumber =     "1572654",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/2689561?origin=pubexport",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}

@Article{Reyssat:1987:AMA,
  author =       "{\'E}ric Reyssat",
  title =        "Approximation des moyennes
                 arithm{\'e}tico--g{\'e}om{\'e}triques. ({French})
                 [{Approximation} of arithmetic--geometric means]",
  journal =      j-ENSEIGN-MATH-2,
  volume =       "33",
  number =       "3--4",
  pages =        "175--181",
  year =         "1987",
  CODEN =        "ENMAAR",
  ISSN =         "0013-8584 (print), 2309-4672 (electronic)",
  MRclass =      "11J82 (11B83 11F11)",
  MRnumber =     "925983",
  MRreviewer =   "John H. Loxton",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "L'Enseignement Math{\'e}matique. Revue Internationale.
                 IIe S{\'e}rie",
  journal-URL =  "http://www.e-periodica.ch/digbib/vollist?var=true&UID=ens-001",
  language =     "French",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Seiffert:1987:WZG,
  author =       "H.-J. Seiffert",
  title =        "{Werte zwischen dem geometrischen und dem
                 arithmetischen Mittel zweier Zahlen}. ({German})
                 [{Values} between the geometric and the arithmetic mean
                 of two numbers]",
  journal =      j-ELEM-MATH,
  volume =       "42",
  number =       "4",
  pages =        "105--107",
  year =         "1987",
  ISSN =         "0013-6018 (print), 1420-8962 (electronic)",
  ISSN-L =       "0013-6018",
  MRclass =      "26D20",
  MRnumber =     "896120",
  MRreviewer =   "L. Losonczi",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elemente der Mathematik. Revue de Math{\'e}matiques
                 {\'E}l{\'e}mentaires. Rivista de Matematica
                 Elementare",
  language =     "German",
}

@Article{Sen:1987:WDA,
  author =       "Pranab Kumar Sen",
  title =        "What do the arithmetic, geometric and harmonic means
                 tell us in length-biased sampling?",
  journal =      j-STAT-PROB-LETT,
  volume =       "5",
  number =       "2",
  pages =        "95--98",
  year =         "1987",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/0167-7152(87)90062-9",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "62E10 (62E20)",
  MRnumber =     "882342",
  MRreviewer =   "Zhi-Dong Bai",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
}

@Article{Almkvist:1988:GLR,
  author =       "Gert Almkvist and Bruce Berndt",
  title =        "{Gauss}, {Landen}, {Ramanujan}, the
                 Arithmetic--Geometric Mean, Ellipses, $ \pi $, and the
                 {{\booktitle{Ladies Diary}}}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "95",
  number =       "7",
  pages =        "585--608",
  month =        aug # "\slash " # sep,
  year =         "1988",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2323302",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "01A50 (01A55 01A60 33A25)",
  MRnumber =     "966232; 89j:01028",
  MRreviewer =   "R. A. Askey",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib; JSTOR
                 database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Alzer:1988:UGA,
  author =       "Horst Alzer",
  title =        "{Ungleichungen f{\"u}r geometrische und arithmetische
                 Mittelwerte}. ({German}) [{Inequalities} for geometric
                 and arithmetic averages]",
  journal =      "Nederl. Akad. Wetensch. Indag. Math.",
  volume =       "50",
  number =       "4",
  pages =        "365--374",
  year =         "1988",
  ISSN =         "0019-3577, 0023-3358",
  MRclass =      "26D20",
  MRnumber =     "976521",
  MRreviewer =   "Yisong Yang",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Koninklijke Nederlandse Akademie van Wetenschappen.
                 Indagationes Mathematicae",
  language =     "German",
}

@Article{Askey:1988:BRP,
  author =       "Richard Askey",
  title =        "Reviews: {{\em Pi and the AGM}}, by {Jonathan M.
                 Borwein and Peter B. Borwein}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "95",
  number =       "9",
  pages =        "895--897",
  month =        nov,
  year =         "1988",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Sat Aug 13 18:09:13 MDT 2016",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2322925",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  keywords =     "AGM (arithmetic--geometric mean)",
}

@Article{Berndt:1988:BRJ,
  author =       "Bruce C. Berndt",
  title =        "Book Review: {Jonathan M. Borwein and Peter B.
                 Borwein, \booktitle{Pi and the AGM --- A Study of
                 Analytic Number Theory and Computational Complexity},
                 Canadian Mathematical Society Series of Mono- graphs
                 and Advanced Texts, Wiley, New York, 1987, xv + 414
                 pp., 24 cm. Price \$49.95}",
  journal =      j-MATH-COMPUT,
  volume =       "50",
  number =       "181",
  pages =        "352--354",
  month =        jan,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Sat Aug 13 18:09:13 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/2007942",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Unpublished{Borwein:1988:AGMa,
  author =       "Jonathan M. Borwein",
  title =        "The arithmetic--geometric mean of {Gauss} and
                 {Legendre}: An Excursion",
  day =          "13",
  month =        may,
  year =         "1988",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Distinguished Lecturer Series, University of Delaware,
                 Newark, DE, USA.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:1988:AGMb,
  author =       "Jonathan M. Borwein",
  title =        "The arithmetic--geometric mean of {Gauss} and
                 {Legendre}: An Excursion",
  day =          "14",
  month =        jun,
  year =         "1988",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, University of Newcastle, Newcastle, NSW,
                 Australia.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:1988:AGMc,
  author =       "Jonathan M. Borwein",
  title =        "The arithmetic--geometric mean of {Gauss} and
                 {Legendre}: An Excursion",
  day =          "27",
  month =        jun,
  year =         "1988",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, University of New England, Armidale, NSW,
                 Australia.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:1988:AGMd,
  author =       "Jonathan M. Borwein",
  title =        "The arithmetic--geometric mean of {Gauss} and
                 {Legendre}: An Excursion",
  day =          "27",
  month =        jul,
  year =         "1988",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, Auckland University, Auckland, New
                 Zealand.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:1988:AGMe,
  author =       "Jonathan M. Borwein",
  title =        "The arithmetic--geometric mean of {Gauss} and
                 {Legendre}: An Excursion",
  day =          "12",
  month =        sep,
  year =         "1988",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, Macquarie University, Sydney, NSW,
                 Australia.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:1988:BFD,
  author =       "Jonathan M. Borwein",
  title =        "{Borchardt}'s four-dimensional arithmetic--geometric
                 mean",
  day =          "14",
  month =        sep,
  year =         "1988",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Seminar, Macquarie University, Sydney, NSW,
                 Australia.",
  acknowledgement = ack-nhfb,
}

@TechReport{Borwein:1988:CCJ,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "A Cubic Counterpart of {Jacobi}'s Identity and the
                 {AGM}",
  type =         "Report",
  institution =  "Department of Mathematics, Statistics and Computing
                 Science, Dalhousie University",
  address =      "Halifax, NS B3H 3J5, Canada",
  pages =        "20",
  day =          "31",
  month =        dec,
  year =         "1988",
  bibdate =      "Fri Nov 11 07:03:04 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  abstract =     "We produce cubic analogues of Jacobi's celebrated
                 theta function identity and of the
                 arithmetic--geometric mean iteration of Gauss and
                 Legendre. The iteration in question is $ a_{n + 1} =
                 (a_n + 2 b_n) / 3 $ and $ b_{n + 1} = \sqrt
                 [3]{b_n((a_n^2 + a_n b_n + b_n^2) / 3)} $. The limit of
                 this iteration is identified in terms of the
                 hypergeometric function $_2 F_1 (1 / 3, 2 / 3; 1;
                 \cdot)$ which supports a particularly simple cubic
                 transformation.",
  acknowledgement = ack-nhfb,
  keywords =     "$\pi$; arithmetic--geometric mean (AGM); cubic
                 transformations; generalised elliptic functions;
                 hypergeometric functions; mean iterations; theta
                 functions",
}

@Article{Bost:1988:MAG,
  author =       "Jean-Beno{\^{\i}}t Bost and Jean-Fran{\c{c}}ois
                 Mestre",
  title =        "Moyenne arithm{\'e}tico--g{\'e}om{\'e}trique et
                 p{\'e}riodes des courbes de genre $1$ et $2$.
                 ({French}) [{Arithmetic--geometric} mean and periods of
                 the curves of genus $1$ and $2$]",
  journal =      j-GAZ-MATH,
  volume =       "38",
  number =       "38",
  pages =        "36--64",
  year =         "1988",
  ISSN =         "0224-8999",
  MRclass =      "14K20 (11F03 11G05)",
  MRnumber =     "970659",
  MRreviewer =   "Reinhard B{\"o}lling",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Gazette des Math{\'e}maticiens",
  language =     "French",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Hurley:1988:RCP,
  author =       "Donal Hurley",
  title =        "Recent computations of $ \pi $",
  journal =      j-IRISH-MATH-SOC-BULL,
  volume =       "21",
  number =       "??",
  pages =        "38--44",
  year =         "1988",
  ISSN =         "0791-5578",
  MRclass =      "11Y60 (01A50 01A55 01A60 11-03)",
  MRnumber =     "988289 (90e:11194)",
  MRreviewer =   "Kenneth A. Jukes",
  bibdate =      "Mon Apr 25 16:20:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Irish Mathematical Society Bulletin",
  journal-URL =  "https://www.maths.tcd.ie/pub/ims/bulletin/",
  keywords =     "agm (arithmetic--geometric mean); Brent--Salamin
                 algorithm (1976); Johann Dase (1824--1861); John Machin
                 (1680--1752)",
  remark =       "No issues before 1995 are available online at
                 http://www.maths.tcd.ie/pub/ims/bulletin/index.php.",
}

@InProceedings{Kanada:1988:VMA,
  author =       "Yasumasa Kanada",
  booktitle =    "Proceedings of Supercomputing 88. Vol. II: Science and
                 Applications",
  title =        "Vectorization of multiple-precision arithmetic program
                 and 201,326,000 decimal digits of {$ \pi $}
                 calculation",
  crossref =     "Martin:1988:SPN",
  volume =       "2",
  pages =        "117--128",
  year =         "1988",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  abstract =     "More than 200 million decimal places of {$ \pi $} were
                 calculated using an arithmetic geometric mean formula
                 independently discovered by E. Salamin and R. P. Brent
                 in 1976. Correctness of the calculation was verified
                 through Borwein's quartic convergent formula developed
                 in 1983. The computation took CPU times of 5 hours 57
                 minutes for the main calculation and 7 hours 30 minutes
                 for the verification calculation on the HITAC S-820
                 model 80 supercomputer with 256 MB of main memory and 3
                 GB of high speed semiconductor storage, Extended
                 Storage, to shorten I/O time.\par Computation was
                 completed in 27th of January 1988. At that day two
                 programs generated values up to $ 3 \times 2^{26} $,
                 about 201 million. The two results agreed except for
                 the last 21 digits. These results also agree with the
                 133,554,000 places of calculation of $ \pi $ which was
                 done by the author in January 1987. Compare to the
                 record in 1987, 50\% more decimal digits were
                 calculated with about $ 1 / 6 $ of CPU time.\par
                 Computation was performed with real arithmetic based
                 vectorized Fast Fourier Transform (FFT) multiplier and
                 newly vectorized multiple-precision add, subtract and
                 (single word) constant multiplication programs.
                 Vectorizations for the later cases were realized
                 through first order linear recurrence vector
                 instruction on the S-820. Details of the computation
                 and statistical tests on the first 200 million digits
                 of $ \pi - 3 $ are reported.",
  acknowledgement = ack-nhfb,
  classification = "C4190 (Other numerical methods); C7310
                 (Mathematics)",
  corpsource =   "Comput. Centre, Tokyo Univ., Japan",
  keywords =     "arithmetic geometric mean formula; Borwein's quartic
                 convergent formula; fast Fourier transform; fast
                 Fourier transforms; first order linear recurrence
                 vector instruction; HITAC S-820 model 80 supercomputer;
                 mathematics computing; multiple-precision arithmetic
                 program; multiplier; parallel processing; pi
                 calculation; S-820; vectorization",
  sponsororg =   "IEEE; ACM SIGARCH",
  treatment =    "P Practical",
}

@Article{Martins:1988:AGM,
  author =       "J. S. Martins",
  title =        "Arithmetic and geometric means, an application to
                 {Lorentz} sequence spaces",
  journal =      j-MATH-NACHR,
  volume =       "139",
  pages =        "281--288",
  year =         "1988",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19881390125",
  ISSN =         "0025-584X",
  MRclass =      "40A05 (26D20 40H05 46A45)",
  MRnumber =     "978126",
  MRreviewer =   "Christian Samuel",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}

@Article{Montuchi:1988:BTE,
  author =       "Paolo Montuchi and Warren Page",
  title =        "Behold! {Two} Extremum Problems (and the
                 {Arithmetic--Geometic Mean Inequality})",
  journal =      j-COLLEGE-MATH-J,
  volume =       "19",
  number =       "4",
  pages =        "347--347",
  month =        sep,
  year =         "1988",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.1988.11973136",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:50:45 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/07468342.1988.11973136",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  onlinedate =   "30 Jan 2018",
}

@Article{Nishiwada:1988:HSA,
  author =       "Kimimasa Nishiwada",
  title =        "A holomorphic structure of the arithmetic--geometric
                 mean of {Gauss}",
  journal =      j-PROC-JAPAN-ACAD-SER-A-MATH-SCI,
  volume =       "64",
  number =       "9",
  pages =        "322--324",
  year =         "1988",
  CODEN =        "PJAADT",
  ISSN =         "0386-2194",
  MRclass =      "30B99",
  MRnumber =     "979233",
  MRreviewer =   "D. C. Russell",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://projecteuclid.org/euclid.pja/1195513088",
  acknowledgement = ack-nhfb,
  fjournal =     "Japan Academy. Proceedings. Series A. Mathematical
                 Sciences",
  journal-URL =  "http://projecteuclid.org/pja",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Nussbaum:1988:AGM,
  author =       "Roger D. Nussbaum and Joel E. Cohen",
  title =        "The arithmetic--geometric mean and its generalizations
                 for noncommuting linear operators",
  journal =      j-ANN-SC-NORM-SUPER-PISA-CL-SCI,
  volume =       "15",
  number =       "2",
  pages =        "239--308 (1989)",
  year =         "1988",
  CODEN =        "PSNAAI",
  ISSN =         "0391-173x (print), 2036-2145 (electronic)",
  ISSN-L =       "0391-173X",
  MRclass =      "47B15 (26A18 47A60 47H07)",
  MRnumber =     "1007399",
  MRreviewer =   "T. Ando",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.numdam.org/item?id=ASNSP_1988_4_15_2_239_0",
  acknowledgement = ack-nhfb,
  fjournal =     "Annali della Scuola Normale Superiore di Pisa. Classe
                 di Scienze. Serie IV",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Schaumberger:1988:GFA,
  author =       "Norman Schaumberger",
  title =        "A General Form of the Arithmetic-Geometric Mean
                 Inequality via the Mean Value Theorem",
  journal =      j-COLLEGE-MATH-J,
  volume =       "19",
  number =       "2",
  pages =        "172--173",
  month =        mar,
  year =         "1988",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.1988.11973110",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:50:41 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/07468342.1988.11973110",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  onlinedate =   "30 Jan 2018",
}

@Article{Wang:1988:IRA,
  author =       "Chung-Shin Wang and Gou Sheng Yang",
  title =        "Inequalities related to the arithmetic and geometric
                 means",
  journal =      j-TAMKANG-J-MATH,
  volume =       "19",
  number =       "2",
  pages =        "79--86",
  year =         "1988",
  ISSN =         "0049-2930 (print), 2073-9826 (electronic)",
  ISSN-L =       "2073-9826",
  MRclass =      "26D20",
  MRnumber =     "996886",
  MRreviewer =   "L. Losonczi",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tamkang Journal of Mathematics",
  journal-URL =  "http://journals.math.tku.edu.tw/index.php/TKJM",
}

@Article{Wimp:1988:BRP,
  author =       "Jet Wimp",
  title =        "Book Review: {{\booktitle{Pi and the AGM: a Study in
                 Analytic Number Theory and Computational Complexity}}
                 (Jonathan M. Borwein and Peter B. Borwein)}",
  journal =      j-SIAM-REVIEW,
  volume =       "30",
  number =       "3",
  pages =        "530--533",
  month =        sep,
  year =         "1988",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1030128",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Aug 13 18:09:13 MDT 2016",
  bibsource =    "http://epubs.siam.org/toc/siread/30/3;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://www.jstor.org/stable/2030735",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "September 1988",
}

@Article{Alzer:1989:RAM,
  author =       "Horst Alzer",
  title =        "A refinement of the arithmetic mean--geometric mean
                 inequality",
  journal =      "Rad. Mat.",
  volume =       "5",
  number =       "2",
  pages =        "231--235",
  year =         "1989",
  ISSN =         "0352-6100",
  MRclass =      "26D15",
  MRnumber =     "1050892",
  MRreviewer =   "E. Thandapani",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Radovi Matemati{\v{c}}ki",
}

@Article{Borwein:1989:MI,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "On the Mean Iteration $ (a, b) \leftarrow \big (\frac
                 {a + 3b}{4}, \frac {\sqrt {ab} + b}{2} \big) $",
  journal =      j-MATH-COMPUT,
  volume =       "53",
  number =       "187",
  pages =        "311--326",
  month =        jul,
  year =         "1989",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2008364",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "30D05 (33A25)",
  MRnumber =     "968148, 90a:30075",
  MRreviewer =   "Carl C. Cowen",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  URL =          "http://docserver.carma.newcastle.edu.au/1586/",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Dept. of Math. Stat. and Comput. Sci., Dalhousie
                 Univ., Halifax, NS, Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computation; convergence of numerical methods;
                 converging process; iterative methods; iterative
                 process; limit; mean iteration; nontrivial
                 identifications; quadratically; symbolic; uniformizing
                 parameters",
  treatment =    "T Theoretical or Mathematical",
}

@Unpublished{Borwein:1989:PAG,
  author =       "Jonathan M. Borwein",
  title =        "Pi and the arithmetic--geometric mean",
  day =          "14",
  month =        apr,
  year =         "1989",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, Rutger's University, New Brunswick, NJ,
                 USA.",
  acknowledgement = ack-nhfb,
}

@Article{Henniart:1989:MAG,
  author =       "Guy Henniart and Jean-Fran{\c{c}}ois Mestre",
  title =        "Moyenne arithm{\'e}tico--g{\'e}om{\'e}trique
                 $p$-adique. ({French}) [$p$-{Adic}
                 arithmetic--geometric mean]",
  journal =      j-C-R-ACAD-SCI-I,
  volume =       "308",
  number =       "13",
  pages =        "391--395",
  year =         "1989",
  CODEN =        "CASMEI",
  ISSN =         "0249-6291",
  ISSN-L =       "0764-4442",
  MRclass =      "11G07 (11F85 11Y99 14G20)",
  MRnumber =     "992515",
  MRreviewer =   "Glenn Stevens",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus des S{\'e}ances de l'Acad{\'e}mie des
                 Sciences. S{\'e}rie I. Math{\'e}matique",
  language =     "French",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Nelsen:1989:RMS,
  author =       "Roger B. Nelsen",
  title =        "The Root Mean Square-Arithmetic Mean--Geometric
                 Mean-Harmonic Mean Inequality",
  journal =      j-COLLEGE-MATH-J,
  volume =       "20",
  number =       "3",
  pages =        "231--231",
  month =        may,
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.1989.11973236",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:50:54 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/07468342.1989.11973236",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  onlinedate =   "30 Jan 2018",
}

@Article{Peetre:1989:GAG,
  author =       "Jaak Peetre",
  title =        "Generalizing the arithmetic geometric mean---a hapless
                 computer experiment",
  journal =      j-INT-J-MATH-MATH-SCI,
  volume =       "12",
  number =       "2",
  pages =        "235--245",
  year =         "1989",
  DOI =          "https://doi.org/10.1155/S016117128900027X",
  ISSN =         "0161-1712 (print), 1687-0425 (electronic)",
  ISSN-L =       "0161-1712",
  MRclass =      "26E99 (01A55 26-03)",
  MRnumber =     "994905",
  MRreviewer =   "Peter Borwein",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
  journal-URL =  "https://www.hindawi.com/journals/ijmms/",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Sala:1989:TJA,
  author =       "Kenneth L. Sala",
  title =        "Transformations of the {Jacobian} amplitude function
                 and its calculation via the arithmetic--geometric
                 mean",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "20",
  number =       "6",
  pages =        "1514--1528",
  month =        nov,
  year =         "1989",
  CODEN =        "SJMAAH",
  DOI =          "https://doi.org/10.1137/0520100",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33A25 (42A16 70D99)",
  MRnumber =     "1019316; 90j:33003",
  MRreviewer =   "J. M. H. Peters",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/20/6;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Schaumberger:1989:GI,
  author =       "Norman Schaumberger",
  title =        "The {AM-GM} Inequality via $ x^{1 / x} $",
  journal =      j-COLLEGE-MATH-J,
  volume =       "20",
  number =       "4",
  pages =        "320--320",
  month =        sep,
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.1989.11973249",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:50:55 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/07468342.1989.11973249",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  onlinedate =   "30 Jan 2018",
}

@Article{Alzer:1990:CAM,
  author =       "Horst Alzer",
  title =        "A converse of the arithmetic mean--geometric mean
                 inequality",
  journal =      "Rev. Un. Mat. Argentina",
  volume =       "36",
  pages =        "146--151 (1992)",
  year =         "1990",
  ISSN =         "0041-6932",
  MRclass =      "26D15",
  MRnumber =     "1265703",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Revista de la Uni{\'o}n Matem{\'a}tica Argentina",
}

@Article{Alzer:1990:GGA,
  author =       "Horst Alzer",
  title =        "{{\"U}ber gewichtete geometrische und arithmetische
                 Mittelwerte}. ({German}) [{On} overweighted geometric
                 and arithmetic mean values]",
  journal =      "Anz. {\"O}sterreich. Akad. Wiss. Math.-Natur. Kl.",
  volume =       "127",
  pages =        "33--36 (1991)",
  year =         "1990",
  MRclass =      "26D20",
  MRnumber =     "1112640",
  MRreviewer =   "P. S. Bullen",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{\"O}sterreichische Akademie der Wissenschaften.
                 Mathematisch-Naturwissenschaftliche Klasse. Anzeiger",
  language =     "German",
}

@Article{Alzer:1990:IAG,
  author =       "Horst Alzer",
  title =        "Inequalities for arithmetic, geometric and harmonic
                 means",
  journal =      j-BULL-LOND-MATH-SOC,
  volume =       "22",
  number =       "4",
  pages =        "362--366",
  year =         "1990",
  CODEN =        "LMSBBT",
  DOI =          "https://doi.org/10.1112/blms/22.4.362",
  ISSN =         "0024-6093 (print), 1469-2120 (electronic)",
  ISSN-L =       "0024-6093",
  MRclass =      "26D15",
  MRnumber =     "1058313",
  MRreviewer =   "P. S. Bullen",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bulletin of the London Mathematical Society",
  journal-URL =  "http://blms.oxfordjournals.org/content/by/year",
}

@Article{Alzer:1990:LBD,
  author =       "Horst Alzer",
  title =        "A lower bound for the difference between the
                 arithmetic and geometric means",
  journal =      j-NIEUW-ARCHIEF-WISKUNDE-4,
  volume =       "8",
  number =       "2",
  pages =        "195--197",
  year =         "1990",
  CODEN =        "NAWIA7",
  ISSN =         "0028-9825",
  MRclass =      "26D15",
  MRnumber =     "1085159",
  MRreviewer =   "P. S. Bullen",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Nieuw Archief voor Wiskunde. Vierde Serie",
}

@Article{Alzer:1990:SAM,
  author =       "Horst Alzer",
  title =        "Sharpenings of the arithmetic mean--geometric mean
                 inequality",
  journal =      j-CONG-NUM,
  volume =       "75",
  pages =        "63--66",
  year =         "1990",
  ISSN =         "0384-9864",
  MRclass =      "26D20",
  MRnumber =     "1069163",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Congressus Numerantium. A Conference Journal on
                 Numerical Themes",
  remark =       "Proceedings of the Nineteenth Manitoba Conference on
                 Numerical Mathematics and Computing (Winnipeg, MB,
                 1989).",
}

@Article{Alzer:1990:WAG,
  author =       "H. Alzer",
  title =        "On weighted arithmetic, geometric and harmonic mean
                 values",
  journal =      "Glas. Mat. Ser. III",
  volume =       "25(45)",
  number =       "2",
  pages =        "279--285",
  year =         "1990",
  ISSN =         "0017-095X",
  MRclass =      "26D15",
  MRnumber =     "1243732",
  MRreviewer =   "Hiroshi Haruki",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Glasnik Matemati{\v{c}}ki. Serija III",
}

@Article{Chuan:1990:NIA,
  author =       "Hao Zhi Chuan",
  title =        "Note on the inequality of the arithmetic and geometric
                 means",
  journal =      j-PAC-J-MATH,
  volume =       "143",
  number =       "1",
  pages =        "43--46",
  year =         "1990",
  CODEN =        "PJMAAI",
  ISSN =         "0030-8730 (print), 1945-5844 (electronic)",
  ISSN-L =       "0030-8730",
  MRclass =      "26D15 (15A45)",
  MRnumber =     "1047400",
  MRreviewer =   "J. S{\'a}ndor",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://projecteuclid.org/euclid.pjm/1102646201",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Mathematics",
  journal-URL =  "http://msp.org/pjm",
}

@Article{Nussbaum:1990:CPG,
  author =       "Roger D. Nussbaum and Joel E. Cohen",
  title =        "Convexity properties of generalizations of the
                 arithmetic--geometric mean",
  journal =      j-NUMER-FUNCT-ANAL-OPTIM,
  volume =       "11",
  number =       "1--2",
  pages =        "33--44",
  year =         "1990",
  CODEN =        "NFAODL",
  DOI =          "https://doi.org/10.1080/01630569008816359",
  ISSN =         "0163-0563",
  MRclass =      "26E05 (39B52 46G99 47H99)",
  MRnumber =     "1058775",
  MRreviewer =   "Sever S. Dragomir",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Functional Analysis and Optimization. An
                 International Journal",
  journal-URL =  "http://www.tandfonline.com/loi/lnfa20",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Sandor:1990:IAG,
  author =       "J. S{\'a}ndor",
  title =        "On the inequality of the arithmetic and geometric
                 means",
  journal =      "Bul. {\c{S}}tiin{\c{t}}. Inst. Politehn. Cluj-Napoca
                 Ser. Mat. Mec. Apl. Construc. Ma{\c{s}}.",
  volume =       "33",
  pages =        "109--112",
  year =         "1990",
  MRclass =      "26D15",
  MRnumber =     "1230744",
  MRreviewer =   "B. Crstici",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Buletinul {\c{S}}tiin{\c{t}}ific al Institutului
                 Politehnic Cluj-Napoca. Seria Matematic{\u{a}},
                 Mecanic{\v{a}} Aplicat\v a, Construc{\c{t}}ii de
                 Ma{\c{s}}ini",
}

@Article{Alzer:1991:NAM,
  author =       "Horst Alzer",
  title =        "A note on the arithmetic mean-geometric mean
                 inequality",
  journal =      "Ann. Univ. Sci. Budapest. E{\"o}tv{\"o}s Sect. Math.",
  volume =       "34",
  pages =        "11--13 (1992)",
  year =         "1991",
  ISSN =         "0524-9007",
  MRclass =      "26D15",
  MRnumber =     "1161495",
  MRreviewer =   "L. Losonczi",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annales Universitatis Scientiarum Budapestinensis de
                 Rolando E{\"o}tv{\"o}s Nominatae. Sectio Mathematica",
}

@Article{Borwein:1991:CCJ,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "A cubic counterpart of {Jacobi}'s identity and the
                 {AGM}",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "323",
  number =       "2",
  pages =        "691--701",
  month =        feb,
  year =         "1991",
  CODEN =        "TAMTAM",
  DOI =          "https://doi.org/10.2307/2001551",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "33C75 (11F11 11Y60 33C05)",
  MRnumber =     "1010408",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1578/;
                 http://www.jstor.org/stable/2001551",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/tran/",
}

@Article{Bullett:1991:DAG,
  author =       "Shaun Bullett",
  title =        "Dynamics of the arithmetic--geometric mean",
  journal =      j-TOPOLOGY,
  volume =       "30",
  number =       "2",
  pages =        "171--190",
  year =         "1991",
  CODEN =        "TPLGAF",
  DOI =          "https://doi.org/10.1016/0040-9383(91)90004-N",
  ISSN =         "0040-9383 (print), 1879-3215 (electronic)",
  ISSN-L =       "0040-9383",
  MRclass =      "58F08 (58F23)",
  MRnumber =     "1098912",
  MRreviewer =   "Andrew Osbaldestin",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/004093839190004N",
  acknowledgement = ack-nhfb,
  fjournal =     "Topology. An International Journal of Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00409383",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Carlson:1991:IAL,
  author =       "B. C. Carlson and M. Vuorinen",
  title =        "Inequality of the {AGM} and the Logarithmic Mean",
  journal =      j-SIAM-REVIEW,
  volume =       "33",
  number =       "4",
  pages =        "655--655",
  month =        "????",
  year =         "1991",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1033141",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:54:57 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/33/4;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "December 1991",
}

@Article{Haruki:1991:NCA,
  author =       "Hiroshi Haruki",
  title =        "New characterizations of the arithmetic--geometric
                 mean of {Gauss} and other well-known mean values",
  journal =      j-PUBL-MATH-DEBRECEN,
  volume =       "38",
  number =       "3--4",
  pages =        "323--332",
  year =         "1991",
  CODEN =        "PUMAAR",
  ISSN =         "0033-3883 (print), 2064-2849 (electronic)",
  MRclass =      "39B22 (26D99)",
  MRnumber =     "1113240",
  MRreviewer =   "Zsolt P{\'a}les",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Publicationes Mathematicae Debrecen",
  journal-URL =  "http://publi.math.unideb.hu/",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Lingappaiah:1991:DRG,
  author =       "G. S. Lingappaiah",
  title =        "Distribution of the ratio of geometric mean to
                 arithmetic mean in a sample from a two-piece double
                 exponential distribution",
  journal =      "Math. Balkanica (N.S.)",
  volume =       "5",
  number =       "1",
  pages =        "76--80",
  year =         "1991",
  ISSN =         "0205-3217",
  MRclass =      "62E15",
  MRnumber =     "1136221",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Balkanica. New Series",
}

@Article{Szyszkowicz:1991:PGL,
  author =       "Mieczyslaw Szyszkowicz",
  title =        "Patterns generated by logical operators",
  journal =      j-COMPUTERS-AND-GRAPHICS,
  volume =       "15",
  number =       "2",
  pages =        "299--300",
  year =         "1991",
  CODEN =        "COGRD2",
  ISSN =         "0097-8493 (print), 1873-7684 (electronic)",
  ISSN-L =       "0097-8493",
  bibdate =      "Fri Feb 07 10:57:32 1997",
  bibsource =    "Compendex database; Graphics/imager/imager.91.bib;
                 Graphics/siggraph/91.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/compgraph.bib",
  acknowledgement = ack-nhfb,
  classification = "723; 921",
  fjournal =     "Computers \& Graphics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00978493",
  journalabr =   "Comput Graphics (Pergamon)",
  keywords =     "Aesthetic Patterns; Arithmetic Geometric Mean
                 Iterations; Computer Graphics; Computer Metatheory ---
                 Formal Logic; Logical Operators; Mathematical
                 Techniques --- Iterative Methods; Research",
}

@Article{Wazwaz:1991:MNM,
  author =       "Abdul-Majid Wazwaz",
  title =        "Modified numerical methods based on arithmetic and
                 geometric means",
  journal =      j-APPL-MATH-LETT,
  volume =       "4",
  number =       "3",
  pages =        "49--52",
  year =         "1991",
  CODEN =        "AMLEEL",
  DOI =          "https://doi.org/10.1016/0893-9659(91)90034-S",
  ISSN =         "0893-9659 (print), 1873-5452 (electronic)",
  ISSN-L =       "0893-9659",
  MRclass =      "65L06 (65D32)",
  MRnumber =     "1101874",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics Letters. An International Journal
                 of Rapid Publication",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08939659",
}

@InCollection{Alzer:1992:IPA,
  author =       "Horst Alzer",
  booktitle =    "General inequalities, 6 ({Oberwolfach}, 1990)",
  title =        "Inequalities for pseudo-arithmetic and geometric
                 means",
  volume =       "103",
  publisher =    "Birkh{\"a}user, Basel",
  pages =        "5--16",
  year =         "1992",
  DOI =          "https://doi.org/10.1007/978-3-0348-7565-3_2",
  MRclass =      "26D15",
  MRnumber =     "1212992",
  MRreviewer =   "L. Losonczi",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "Internat. Ser. Numer. Math.",
  acknowledgement = ack-nhfb,
}

@Article{Alzer:1992:SAM,
  author =       "Horst Alzer",
  title =        "A sharpening of the arithmetic mean-geometric mean
                 inequality",
  journal =      j-UTIL-MATH,
  volume =       "41",
  pages =        "249--252",
  year =         "1992",
  CODEN =        "UTMADA",
  ISSN =         "0315-3681",
  MRclass =      "26D15",
  MRnumber =     "1162530",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Utilitas Mathematica. An International Journal of
                 Discrete and Combinatorial Mathematics, and Statistical
                 Design",
}

@Article{Braden:1992:IAL,
  author =       "B. Braden and B. Danloy and F. Schmidt",
  title =        "Inequality of the {AGM} and the Logarithmic Mean",
  journal =      j-SIAM-REVIEW,
  volume =       "34",
  number =       "4",
  pages =        "653--654",
  month =        "????",
  year =         "1992",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "December 1992",
}

@Article{Cohen:1992:RAG,
  author =       "Joel E. Cohen and Thomas M. Liggett",
  title =        "Random arithmetic--geometric means and random pi:
                 observations and conjectures",
  journal =      j-STOCH-PROC-APPL,
  volume =       "41",
  number =       "2",
  pages =        "261--271",
  year =         "1992",
  CODEN =        "STOPB7",
  DOI =          "https://doi.org/10.1016/0304-4149(92)90126-B",
  ISSN =         "0304-4149 (print), 1879-209x (electronic)",
  ISSN-L =       "0304-4149",
  MRclass =      "60J05 (65D20 65U05)",
  MRnumber =     "1164179",
  MRreviewer =   "M. Iosifescu",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/030441499290126B",
  abstract =     "Two random versions of the arithmetic--geometric mean
                 of Gauss, Lagrange and Legendre are defined. Almost
                 sure convergence and nondegeneracy are proved. These
                 random arithmetic--geometric means in turn define two
                 random versions of $ \pi $. Based on numerical
                 simulations, inequalities and equalities are
                 conjectured. A special case is proved. Further proofs
                 are invited.",
  acknowledgement = ack-nhfb,
  fjournal =     "Stochastic Processes and Their Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03044149",
  keywords =     "elliptic integrals; Markov processes with discrete
                 parameter; nonlinear iteration; pi",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Unpublished{Dijkstra:1992:AMG,
  author =       "Edsger W. Dijkstra",
  title =        "The arithmetic mean and the geometric mean",
  month =        oct,
  year =         "1992",
  bibdate =      "Mon Mar 16 08:14:00 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Circulated privately.",
  URL =          "http://www.cs.utexas.edu/users/EWD/ewd11xx/EWD1140.PDF",
  acknowledgement = ack-nhfb,
  filesize =     "75 KB",
  oldlabel =     "EWD:EWD1140",
}

@Article{Gauss:1992:AGM,
  author =       "Karl F. Gauss",
  title =        "La media aritm{\'e}tico geom{\'e}trica [The
                 arithmetic--geometric mean] (de origene propietati
                 busque generalis numerorum mediorum
                 aritmeticorum--geometricorum)",
  journal =      "Bol. Mat.",
  volume =       "23",
  number =       "1--2",
  pages =        "69--79",
  year =         "1992",
  CODEN =        "BOMAD4",
  ISSN =         "0120-0380 (print), 2357-6529 (electronic)",
  ISSN-L =       "0120-0380",
  MRclass =      "01A75 (01A55)",
  MRnumber =     "1221411",
  MRreviewer =   "Thomas Archibald",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Translated from the Latin original by Fabio Hernando
                 Ortiz.",
  URL =          "http://revistas.unal.edu.co/index.php/bolma/article/view/18204",
  acknowledgement = ack-nhfb,
  author-dates = "1777--1855",
  fjournal =     "Bolet{\'\i}n de Matem{\'a}ticas",
  remark =       "The Math Reviews commentary on this article reports
                 some deficiencies and omissions in the translation, and
                 notes that Gauss' Latin title was ``de origene
                 propietatibusque generalibus numerorum mediorum
                 aritmet. geometricorum''.",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Kittaneh:1992:NAG,
  author =       "Fuad Kittaneh",
  title =        "A note on the arithmetic--geometric-mean inequality
                 for matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "171",
  pages =        "1--8",
  year =         "1992",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/0024-3795(92)90247-8",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A42",
  MRnumber =     "1165442",
  MRreviewer =   "Shao Kuan Li",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@InCollection{Roy:1992:CBA,
  author =       "Dilip Roy and S. P. Mukherjee",
  booktitle =    "Contributions to stochastics",
  title =        "Characterizations based on arithmetic, geometric and
                 harmonic means of failure rates",
  publisher =    "Wiley, New York",
  pages =        "178--185",
  year =         "1992",
  MRclass =      "62E10 (62N05)",
  MRnumber =     "1223334",
  MRreviewer =   "Eugenio Regazzini",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Todd:1992:BRB,
  author =       "John Todd and Bill Braden and Bernard Danloy and Frank
                 Schmidt",
  title =        "Book Review: {{\booktitle{Inequality of the AGM and
                 the Logarithmic Mean}} (B. C. Carlson and M.
                 Vuorinen)}",
  journal =      j-SIAM-REVIEW,
  volume =       "34",
  number =       "4",
  pages =        "653--654",
  month =        "????",
  year =         "1992",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1034127",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:55:07 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/34/4;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "December 1992",
}

@Article{Bencze:1993:NPAa,
  author =       "M. Bencze",
  title =        "A new proof of the arithmetic--geometric mean
                 inequality",
  journal =      j-OCTOGON-MATH-MAG,
  volume =       "1",
  number =       "1",
  pages =        "9--10",
  year =         "1993",
  ISSN =         "1222-5657 (print), 2248-1893 (electronic)",
  MRclass =      "26-01 (26D20 40A99)",
  MRnumber =     "1270849",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Octogon Mathematical Magazine",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Bencze:1993:NPAb,
  author =       "Mihaly Bencze and Norman Schaumberger",
  title =        "A New Proof of the Arithmetic--Geometric Mean
                 Inequality",
  journal =      j-MATH-MAG,
  volume =       "66",
  number =       "4",
  pages =        "245",
  year =         "1993",
  CODEN =        "MAMGA8",
  ISSN =         "0025-570X",
  MRclass =      "DML",
  MRnumber =     "1572972",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/2690740?origin=pubexport",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Bhatia:1993:MMF,
  author =       "Rajendra Bhatia and Chandler Davis",
  title =        "More Matrix Forms of the Arithmetic--Geometric Mean
                 Inequality",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "14",
  number =       "1",
  pages =        "132--136",
  month =        jan,
  year =         "1993",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/0614012",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A45 (15A60 47A63)",
  MRnumber =     "1199551; 94b:15017",
  MRreviewer =   "Ching-Tsuan Pan",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Borwein:1993:HAA,
  author =       "J. Borwein and P. Borwein and F. Garvan",
  title =        "Hypergeometric analogues of the arithmetic--geometric
                 mean iteration",
  journal =      j-CONST-APPROX,
  volume =       "9",
  number =       "4",
  pages =        "509--523",
  year =         "1993",
  DOI =          "https://doi.org/10.1007/BF01204654",
  ISSN =         "0176-4276 (print), 1432-0940 (electronic)",
  ISSN-L =       "0176-4276",
  MRclass =      "33C05",
  MRnumber =     "1237931",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1556/;
                 http://link.springer.com/article/10.1007/BF01204654",
  acknowledgement = ack-nhfb,
  fjournal =     "Constructive Approximation. An International Journal
                 for Approximations and Expansions",
  journal-URL =  "http://link.springer.com/journal/365",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@Article{Borwein:1993:ICM,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "Inequalities for Compound Mean Iterations with
                 Logarithmic Asymptotes",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "177",
  number =       "2",
  pages =        "572--582",
  year =         "1993",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1006/jmaa.1993.1278",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "33B99",
  MRnumber =     "1231502",
  MRreviewer =   "P. Anandani",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1553/;
                 http://www.sciencedirect.com/science/article/pii/S0022247X83712783",
  abstract =     "We consider the compound means arising as limits from
                 the arithmetic--geometric mean iteration and related
                 iterations. Each of these iterations possesses a
                 logarithmic asymptote. We show that these limit means
                 satisfy very precise inequalities. These can be deduced
                 in a quite uniform fashion from a `comparison lemma'
                 for compound means.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
}

@Article{Bullett:1993:RSP,
  author =       "Shaun Bullett and Jaroslav Stark",
  title =        "Renormalizing the Simple Pendulum",
  journal =      j-SIAM-REVIEW,
  volume =       "35",
  number =       "4",
  pages =        "631--640",
  month =        dec,
  year =         "1993",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1035140",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "70-01 (33E05 70K99)",
  MRnumber =     "94i:70001",
  MRreviewer =   "Coraci P. Malta",
  bibdate =      "Sat Mar 29 09:55:16 MDT 2014",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/35/4;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  abstract =     "The authors present an elementary scheme for
                 calculating the period of oscillation or rotation of a
                 simple pendulum. It is based on the invariance of the
                 complete elliptic integral of the first kind under the
                 arithmetic--geometric mean iteration. They explain how
                 this scheme can be interpreted as an example of
                 renormalization, a technique with many recent
                 applications in both physics and applied mathematics.",
  acknowledgement = ack-nhfb,
  affiliation =  "Queen Mary and Westfield Coll",
  affiliationaddress = "London, Engl",
  classification = "921.2; 921.3; 921.6; 931.1; 943.1",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "Algorithms; Arithmetic--geometric mean; Elliptic
                 integral; Equations of motion; Hamiltonian formalism;
                 Integration; Iterative methods; Landen's
                 transformation; Mathematical transformations;
                 Oscillations; Pendulums; Renormalization; Rotation",
  onlinedate =   "December 1993",
}

@Article{Dragomir:1993:ETR,
  author =       "Sever Silvestru Dragomir",
  title =        "Errata: ``{Two refinements of the arithmetic
                 mean-geometric mean inequality'' [Nieuw Arch. Wisk.\
                 (4) {\bf 11} (1993), no. 1, 9--12; MR1220829
                 (94c:26025)]}",
  journal =      j-NIEUW-ARCHIEF-WISKUNDE-4,
  volume =       "11",
  number =       "3",
  pages =        "198",
  year =         "1993",
  CODEN =        "NAWIA7",
  ISSN =         "0028-9825",
  MRclass =      "26D15 (26B25)",
  MRnumber =     "1251481",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Nieuw Archief voor Wiskunde. Vierde Serie",
}

@Article{Dragomir:1993:TRA,
  author =       "Sever Silvestru Dragomir",
  title =        "Two refinements of the arithmetic mean-geometric mean
                 inequality",
  journal =      j-NIEUW-ARCHIEF-WISKUNDE-4,
  volume =       "11",
  number =       "1",
  pages =        "9--12",
  year =         "1993",
  CODEN =        "NAWIA7",
  ISSN =         "0028-9825",
  MRclass =      "26D15 (26B25)",
  MRnumber =     "1220829",
  MRreviewer =   "Hiroshi Haruki",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Nieuw Archief voor Wiskunde. Vierde Serie",
}

@Article{Hao:1993:RAG,
  author =       "Zhi Chuan Hao",
  title =        "A refinement of the arithmetic--geometric means
                 inequality",
  journal =      "J. Math. Res. Exposition",
  volume =       "13",
  number =       "1",
  pages =        "84--88",
  year =         "1993",
  CODEN =        "SYPIET",
  ISSN =         "1000-341X",
  MRclass =      "26D15 (26D05)",
  MRnumber =     "1211057",
  MRreviewer =   "Hiroshi Haruki",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Research and Exposition",
  zzbibdate =    "Tue Aug 15 11:03:11 2017",
}

@InCollection{Karmer:1993:MPC,
  author =       "W. Karmer",
  title =        "Multiple-precision computations with result
                 verification",
  crossref =     "Adams:1993:SCA",
  pages =        "325--356",
  month =        "????",
  year =         "1993",
  bibdate =      "Thu Dec 14 17:22:42 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  abstract =     "Multiple-precision real and interval modules for
                 PASCAL-XSC have been developed. These modules are used
                 to illustrate a variety of algorithms for the following
                 purposes: multiple-precision evaluation of the function
                 square root with maximum accuracy, the
                 arithmetic--geometric mean iteration, different methods
                 for the computation of a large number of digits of pi,
                 the computation of elliptic integrals, the computation
                 of guaranteed bounds for the natural logarithm, and the
                 computation of e/sup pi / using a representation of
                 this value by an infinite product. In general,
                 enclosures for the desired values are computed. Due to
                 the concept of overloading of functions and the
                 operator concept of PASCAL-XSC the programs become
                 clear and readable.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe Univ., Germany",
  classification = "C5230 (Digital arithmetic methods); C6140D (High
                 level languages); C7310 (Mathematics)",
  keywords =     "Arithmetic--geometric mean iteration; Elliptic
                 integrals; Enclosures; Function square root; Guaranteed
                 bounds; Infinite product; Interval modules; Maximum
                 accuracy; Multiple-precision evaluation; Natural
                 logarithm; Operator concept; PASCAL-XSC; Result
                 verification",
  pageswhole =   "x + 612",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; High level languages; Mathematics
                 computing; Pascal",
}

@InCollection{Kramer:1993:MPC,
  author =       "Walter Kr{\"a}mer",
  booktitle =    "Mathematics in Science and Engineering: Scientific
                 Computing with Automatic Result Verification",
  title =        "Multiple-Precision Computations with Result
                 Verification",
  volume =       "189",
  publisher =    "Elsevier BV",
  address =      "Amsterdam, The Netherlands",
  pages =        "325--356",
  year =         "1993",
  DOI =          "https://doi.org/10.1016/s0076-5392(08)62851-9",
  bibdate =      "Tue Mar 14 19:20:47 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic--geometric mean iteration; computation of $
                 e^\pi $; computation of a large number of digits of
                 $\pi$; computation of elliptic integrals; computation
                 of guaranteed bounds for the natural logarithm;
                 interval arithmetic; PASCAL-XSC",
}

@Article{Mathias:1993:AGH,
  author =       "Roy Mathias",
  title =        "An arithmetic--geometric-harmonic mean inequality
                 involving {Hadamard} products",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "184",
  pages =        "71--78",
  year =         "1993",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/0024-3795(93)90370-4",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A45 (26D15 47A63)",
  MRnumber =     "1209383",
  MRreviewer =   "Leo Livshits",
  bibdate =      "Tue Aug 15 11:03:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Alzer:1994:NSA,
  author =       "Horst Alzer",
  title =        "Note on special arithmetic and geometric means",
  journal =      "Comment. Math. Univ. Carolin.",
  volume =       "35",
  number =       "2",
  pages =        "409--412",
  year =         "1994",
  ISSN =         "0010-2628 (print), 1213-7243 (electronic)",
  MRclass =      "26D99 (26A99 40A05)",
  MRnumber =     "1286588",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Commentationes Mathematicae Universitatis Carolinae",
}

@Article{Bencze:1994:NPW,
  author =       "M. Bencze",
  title =        "A new proof of the weighted arithmetic--geometric mean
                 inequality",
  journal =      j-OCTOGON-MATH-MAG,
  volume =       "2",
  number =       "1",
  pages =        "17--18",
  year =         "1994",
  ISSN =         "1222-5657 (print), 2248-1893 (electronic)",
  MRclass =      "26D20",
  MRnumber =     "1303995",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Octogon Mathematical Magazine",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Unpublished{Dijkstra:1994:AAA,
  author =       "Edsger W. Dijkstra",
  title =        "The argument about the arithmetic mean and the
                 geometric mean, heuristics included",
  month =        jan,
  year =         "1994",
  bibdate =      "Mon Mar 16 08:14:00 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Circulated privately.",
  URL =          "http://www.cs.utexas.edu/users/EWD/ewd11xx/EWD1171.PDF",
  acknowledgement = ack-nhfb,
  filesize =     "137 KB",
  oldlabel =     "EWD:EWD1171",
}

@Article{Dzhaparidze:1994:SAI,
  author =       "Kacha Dzhaparidze and Ren{\'e} H. P. Janssen",
  title =        "A stochastic approach to an interpolation problem with
                 applications to {Hellinger} integrals and
                 arithmetic--geometric mean relationship",
  journal =      j-CWI-QUARTERLY,
  volume =       "7",
  number =       "3",
  pages =        "245--258",
  year =         "1994",
  ISSN =         "0922-5366",
  MRclass =      "41A05 (41A55)",
  MRnumber =     "1328044",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Centrum voor Wiskunde en Informatica. Centre for
                 Mathematics and Computer Science. CWI Quarterly",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Article{Furuta:1994:NAG,
  author =       "Takayuki Furuta",
  title =        "A note on the arithmetic--geometric mean inequality
                 for every unitarily invariant matrix norm",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "208--209",
  number =       "??",
  pages =        "223--228",
  year =         "1994",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/0024-3795(94)90439-1",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A60",
  MRnumber =     "1287348; 95f:15020",
  MRreviewer =   "Frank Hansen",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0024379594904391",
  abstract =     "We integrate ten unitarily invariant matrix norm
                 inequalities equivalent to the Heinz inequality.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@InCollection{Garvan:1994:CMI,
  author =       "Frank Garvan",
  booktitle =    "The {Rademacher} legacy to mathematics ({University}
                 {Park}, {PA}, 1992)",
  title =        "Cubic modular identities of {Ramanujan},
                 hypergeometric functions and analogues of the
                 arithmetic--geometric mean iteration",
  volume =       "166",
  publisher =    "Amer. Math. Soc., Providence, RI",
  pages =        "245--264",
  year =         "1994",
  DOI =          "https://doi.org/10.1090/conm/166/01633",
  MRclass =      "39B12 (11F11 33C55)",
  MRnumber =     "1284065",
  MRreviewer =   "R. A. Askey",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "Contemp. Math.",
  acknowledgement = ack-nhfb,
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Article{Kedlaya:1994:PMA,
  author =       "Kiran Kedlaya",
  title =        "Proof of a mixed arithmetic-mean, geometric-mean
                 inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "101",
  number =       "4",
  pages =        "355--357",
  year =         "1994",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2975630",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26D15",
  MRnumber =     "1270962",
  MRreviewer =   "F. Holland",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Kittaneh:1994:SOI,
  author =       "Fuad Kittaneh",
  title =        "On some operator inequalities",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "208--209",
  number =       "??",
  pages =        "19--28",
  year =         "1994",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/0024-3795(94)90427-8",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0024379594904278",
  abstract =     "For Hilbert-space operators $S$, $T$ with $S$
                 invertible and self-adjoint, Corach, Porta, and Recht
                 recently proved that $ || S T S^{-1} + S^{-1} T S ||
                 \geq 2 || T ||$. A generalization of this inequality to
                 larger classes of operators and norms is obtained as an
                 immediate consequence of the operator form of the
                 arithmetic--geometric-mean inequality. Some related
                 inequalities are also discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Liu:1994:GLA,
  author =       "Zhi Guo Liu",
  title =        "The geometric, logarithmic, and arithmetic mean
                 inequalities in {$n$} variables",
  journal =      "J. Chengdu Univ. Natur. Sci.",
  volume =       "13",
  number =       "1",
  pages =        "37--41",
  year =         "1994",
  ISSN =         "1004-5422",
  MRclass =      "26D15",
  MRnumber =     "1399044",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Chengdu University. Natural Sciences.
                 Chengdu Daxue Xuebao. Ziran Kexue Ban",
}

@Article{Nishiwada:1994:HSA,
  author =       "Kimimasa Nishiwada",
  title =        "Holomorphic structure of the arithmetic--geometric
                 mean of {Gauss}. {II}",
  journal =      j-PROC-JAPAN-ACAD-SER-A-MATH-SCI,
  volume =       "70",
  number =       "5",
  pages =        "119--122",
  year =         "1994",
  CODEN =        "PJAADT",
  ISSN =         "0386-2194",
  MRclass =      "30B99 (40A05)",
  MRnumber =     "1291164",
  MRreviewer =   "D. C. Russell",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://projecteuclid.org/euclid.pja/1195511045",
  acknowledgement = ack-nhfb,
  fjournal =     "Japan Academy. Proceedings. Series A. Mathematical
                 Sciences",
  journal-URL =  "http://projecteuclid.org/pja",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Article{Sagae:1994:ULB,
  author =       "Masahiko Sagae and Kunio Tanabe",
  title =        "Upper and lower bounds for the
                 arithmetic--geometric-harmonic means of positive
                 definite matrices",
  journal =      j-LIN-AND-MULT-ALGEBRA,
  volume =       "37",
  number =       "4",
  pages =        "279--282",
  year =         "1994",
  CODEN =        "LNMLAZ",
  DOI =          "https://doi.org/10.1080/03081089408818331",
  ISSN =         "0308-1087 (print), 1563-5139 (electronic)",
  ISSN-L =       "0308-1087",
  MRclass =      "15A45 (15A48)",
  MRnumber =     "1310971",
  MRreviewer =   "Frank Hansen",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear and Multilinear Algebra",
  journal-URL =  "http://www.tandfonline.com/loi/glma20",
}

@Article{Vamanamurthy:1994:IM,
  author =       "M. K. Vamanamurthy and M. Vuorinen",
  title =        "Inequalities for Means",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "183",
  number =       "1",
  pages =        "155--166",
  year =         "1994",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1006/jmaa.1994.1137",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X84711371",
  abstract =     "A monotone form of L'Hospital's rule is obtained and
                 applied to derive inequalities between the
                 arithmetic--geometric mean of Gauss, the logarithmic
                 mean, and Stolarsky's identric mean. Some related
                 inequalities are given for complete elliptic
                 integrals.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
}

@Article{Alzer:1995:DII,
  author =       "Horst Alzer",
  title =        "On discrete inequalities involving arithmetic,
                 geometric, and harmonic means",
  journal =      "Rend. Istit. Mat. Univ. Trieste",
  volume =       "27",
  number =       "1-2",
  pages =        "1--9 (1996)",
  year =         "1995",
  ISSN =         "0049-4704",
  MRclass =      "26D15",
  MRnumber =     "1421044",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rendiconti dell'Istituto di Matematica
                 dell'Universit{\`a} di Trieste. An International
                 Journal of Mathematics",
}

@Article{Bencze:1995:NPA,
  author =       "Mih{\'a}ly Bencze",
  title =        "A new proof of the arithmetic--geometric pondered mean
                 inequality",
  journal =      j-OCTOGON-MATH-MAG,
  volume =       "3",
  number =       "1",
  pages =        "16--17",
  year =         "1995",
  ISSN =         "1222-5657 (print), 2248-1893 (electronic)",
  MRclass =      "26D15",
  MRnumber =     "1361852",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Octogon Mathematical Magazine",
}

@Unpublished{Borwein:1995:CAD,
  author =       "Jonathan M. Borwein",
  title =        "The cubic {AGM} discovered",
  day =          "26",
  month =        oct,
  year =         "1995",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Specialist Colloquium Lecture, University of Utrecht,
                 Utrecht, The Netherlands.",
  acknowledgement = ack-nhfb,
}

@Article{Feng:1995:RAG,
  author =       "Ci Huang Feng",
  title =        "A refinement of the arithmetic--geometric mean
                 inequality",
  journal =      "J. Hangzhou Univ. Natur. Sci. Ed.",
  volume =       "22",
  number =       "3",
  pages =        "222--225",
  year =         "1995",
  CODEN =        "HHHPD7",
  ISSN =         "0253-3618",
  MRclass =      "26D15",
  MRnumber =     "1359614",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Hangzhou University. Natural Science
                 Edition. Hangzhou Daxue Xuebao. Ziran Kexue Ban",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Article{Horn:1995:NBH,
  author =       "Roger A. Horn",
  title =        "Norm Bounds for {Hadamard} Products and an
                 Arithmetic--Geometric Mean Inequality for Unitarily
                 Invariant Norms",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "223--224",
  number =       "1--3",
  pages =        "355--361",
  day =          "??",
  month =        jul,
  year =         "1995",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/0024-3795(94)00034-B",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A45 (15A60 47A63)",
  MRnumber =     "1340700; 96h:15020",
  MRreviewer =   "Roy Mathias",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala1990.bib",
  note =         "Special issue honoring Miroslav Fiedler and Vlastimil
                 Pt{\'a}k.",
  URL =          "http://www.sciencedirect.com/science/article/pii/002437959400034B",
  abstract =     "An arithmetic--geometric mean inequality for unitarily
                 invariant norms and matrices, $ 2 || A \star X B ||
                 \leq || A A \star X + X B B \star || $, is an immediate
                 consequence of a basic inequality for singular values
                 of Hadamard products.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Article{Lucht:1995:AGM,
  author =       "Lutz G. Lucht",
  title =        "On the arithmetic--geometric mean inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "102",
  number =       "8",
  pages =        "739--740",
  month =        oct,
  year =         "1995",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2974645",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26D15",
  MRnumber =     "1 357 492",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Article{Mathias:1995:EAG,
  author =       "Roy Mathias",
  title =        "Erratum: ``{An} arithmetic--geometric-harmonic mean
                 inequality involving {Hadamard} products'' [{Linear}
                 {Algebra} {Appl}. {\bf 184} (1993), 71--78; {MR1209383}
                 (94b:15019)]",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "220",
  pages =        "4",
  year =         "1995",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A45 (26D15 47A63)",
  MRnumber =     "1334561",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Matsuda:1995:IPM,
  author =       "Takashi Matsuda",
  title =        "An inductive proof of a mixed arithmetic--geometric
                 mean inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "102",
  number =       "7",
  pages =        "634--637",
  month =        aug # "\slash " # sep,
  year =         "1995",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2974561",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26D15",
  MRnumber =     "1349877; 96h:26021",
  MRreviewer =   "Zsolt P{\'a}les",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Article{Nelsen:1995:PWA,
  author =       "Roger B. Nelsen",
  title =        "Proof without {Words}: {The}
                 {Arithmetic}-{Logarithmic}-{Geometric} {Mean}
                 {Inequality}",
  journal =      j-MATH-MAG,
  volume =       "68",
  number =       "4",
  pages =        "305",
  year =         "1995",
  CODEN =        "MAMGA8",
  ISSN =         "0025-570X",
  MRclass =      "DML",
  MRnumber =     "1573115",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/2690586?origin=pubexport",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}

@Article{Pecaric:1995:RSA,
  author =       "Josip Pe{\v{c}}ari{\'c}",
  title =        "On a recent sharpening of the arithmetic
                 mean---geometric mean inequality",
  journal =      j-UTIL-MATH,
  volume =       "48",
  pages =        "3--4",
  year =         "1995",
  CODEN =        "UTMADA",
  ISSN =         "0315-3681",
  MRclass =      "26D15",
  MRnumber =     "1358587",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Utilitas Mathematica. An International Journal of
                 Discrete and Combinatorial Mathematics, and Statistical
                 Design",
}

@InProceedings{Sole:1995:A,
  author =       "Patrick Sole",
  title =        "{$ D_4 $}, {$ E_6 $}, {$ E_8 $} and the {AGM}",
  crossref =     "Cohen:1995:AAA",
  volume =       "948",
  pages =        "448--455",
  year =         "1995",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/3-540-60114-7_35",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Mar 14 15:36:33 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs1995a.bib",
  abstract =     "We derive Jacobi's quartic identity and the Borweins'
                 cubic identity related to Ramanujan's quadratic modular
                 equation on theta series by lattice enumerative
                 methods. Both identities are instrumental in recent
                 work of the Borweins on the Arithmetic Geometric Mean.
                 Of great use are the constructions of the root lattices
                 $ D_4 $ and $ E_6 $ by binary and ternary codes
                 respectively. A third identity, equally due to the
                 Borweins is also derived in relation to the root
                 lattice $ E_8 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Alzer:1996:PAM,
  author =       "Horst Alzer",
  title =        "A proof of the arithmetic mean--geometric mean
                 inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "103",
  number =       "7",
  pages =        "585--585",
  month =        aug # "\slash " # sep,
  year =         "1996",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2974672",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26D15",
  MRnumber =     "1 404 083",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@TechReport{Borwein:1996:AGM,
  author =       "Jonathan A. Borwein and Petr Lison{\v{e}}k and John A.
                 Macdonald",
  title =        "Arithmetic--Geometric Means Revisited",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "8",
  year =         "1996",
  bibdate =      "Thu Sep 01 10:39:15 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/4/",
  abstract =     "We use Maple's {\tt gfun} library to study the limit
                 formulae for a two-term recurrence (iteration) $ A G_N
                 $, which in the case $ N = 2 $ specializes to the
                 well-known Arithmetic-Geometric Mean iteration of
                 Gauss. Our main aim 1s to independently rediscover and
                 prove the limit formulae for two classical cases ($ N =
                 2, 3$) in a completely automated manner and to open the
                 way for studying the remaining cases ($ N > 3$).",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}

@Article{dalahu:1996:AIA,
  author =       "Ba dalahu",
  title =        "Applications of the inequality for arithmetic means
                 and geometric means in nonlinear programming",
  journal =      "Neimenggu Daxue Xuebao Ziran Kexue",
  volume =       "27",
  number =       "6",
  pages =        "736--739",
  year =         "1996",
  ISSN =         "1000-1638",
  MRclass =      "90C30 (65K05)",
  MRnumber =     "1444556",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Neimenggu Daxue Xuebao. Ziran Kexue. Acta Scientiarum
                 Naturalium Universitatis Neimenggu. Journal of Inner
                 Mongolia University",
}

@InProceedings{Dijkstra:1996:AAA,
  author =       "Edsger W. Dijkstra",
  title =        "The argument about the arithmetic mean and the
                 geometric mean, heuristics included",
  crossref =     "Broy:1996:DPD",
  pages =        "29--32",
  year =         "1996",
  bibdate =      "Wed Mar 18 12:28:57 2015",
  bibsource =    "DBLP;
                 http://dblp.uni-trier.de/db/conf/nato/dpd1996.html#Dijkstra96g;
                 https://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/DBLP/1996.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Unpublished{Dijkstra:1996:AGM,
  author =       "Edsger W. Dijkstra",
  title =        "The arithmetic and geometric means once more",
  month =        feb,
  year =         "1996",
  bibdate =      "Mon Mar 16 08:14:00 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Circulated privately.",
  URL =          "http://www.cs.utexas.edu/users/EWD/ewd12xx/EWD1231.PDF",
  acknowledgement = ack-nhfb,
  filesize =     "63 KB",
  oldlabel =     "EWD:EWD1231",
}

@Article{Kanas:1996:UCC,
  author =       "Stanis{\l}awa Kanas and Adam Lecko",
  title =        "Univalence criteria connected with arithmetic and
                 geometric means. {II}",
  journal =      "Zeszyty Nauk. Politech. Rzeszowskiej Mat.",
  volume =       "20",
  pages =        "49--59",
  year =         "1996",
  ISSN =         "1232-7867",
  MRclass =      "30C80",
  MRnumber =     "1473957",
  MRreviewer =   "William Ma",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Zeszyty Naukowe Politechniki Rzeszowskiej.
                 Matematyka",
}

@InProceedings{Kaufmann:1996:IBMa,
  author =       "Matt Kaufmann and Paolo Pecchiari",
  title =        "Interaction with the {Boyer--Moore} Theorem Prover: a
                 Tutorial Study Using the Arithmetic--Geometric Mean
                 Theorem",
  crossref =     "Zhang:1996:AMI",
  pages =        "181--222",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/978-94-009-1675-3_6",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-94-009-1675-3_6",
  acknowledgement = ack-nhfb,
  remark =       "This chapter presents a formal proof with the
                 Boyer--Moore Theorem Prover that the arithmetic mean of
                 a sequence of natural numbers is greater than or equal
                 to their geometric mean.",
}

@Article{Kaufmann:1996:IBMb,
  author =       "Matt Kaufmann and Paolo Pecchiari",
  title =        "Interaction with the {Boyer--Moore} theorem prover: a
                 tutorial study using the arithmetic--geometric mean
                 theorem",
  journal =      j-J-AUTOM-REASON,
  volume =       "16",
  number =       "1--2",
  pages =        "181--222",
  month =        mar,
  year =         "1996",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1007/BF00244463",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  MRclass =      "68T15 (03B35)",
  MRnumber =     "1390909",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "http://link.springer.com/article/10.1007/BF00244463",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@InProceedings{Luther:1996:CAG,
  author =       "Wolfram Luther and Werner Otten",
  title =        "The Complex Arithmetic--Geometric Mean and
                 Multiple-Precision Matrix Functions",
  crossref =     "Alefeld:1996:SCV",
  pages =        "52--58",
  year =         "1996",
  MRclass =      "65G10 (65H99)",
  MRnumber =     "1394225",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Neuman:1996:TIA,
  author =       "Edward Neuman",
  title =        "Three Inequalities for the Arithmetic, Identric, and
                 Geometric Means",
  journal =      j-SIAM-REVIEW,
  volume =       "38",
  number =       "2",
  pages =        "315--315",
  month =        "????",
  year =         "1996",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1038050",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:55:40 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/38/2;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "June 1996",
}

@Article{Sandor:1996:CIM,
  author =       "J. S{\'a}ndor",
  title =        "On Certain Inequalities for Means, {II}",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "199",
  number =       "2",
  pages =        "629--635",
  year =         "1996",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1006/jmaa.1996.0165",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X96901651",
  abstract =     "A method based on sequences is applied to derive
                 inequalities between the arithmetic--geometric mean of
                 Gauss, the logarithmic mean, and certain other means.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
}

@Article{Stefanski:1996:NAG,
  author =       "L. A. Stefanski",
  title =        "A note on the arithmetic--geometric-harmonic mean
                 inequalities",
  journal =      j-AMER-STAT,
  volume =       "50",
  number =       "3",
  pages =        "246--247",
  year =         "1996",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.2307/2684665",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  MRclass =      "60E15",
  MRnumber =     "1422074",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Alic:1997:AGH,
  author =       "M. Ali{\'c} and B. Mond and J. Pe{\v{c}}ari{\'c} and
                 V. Volenec",
  title =        "The arithmetic--geometric--harmonic-mean and related
                 matrix inequalities",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "264",
  pages =        "55--62",
  year =         "1997",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/S0024-3795(96)00471-5",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A45",
  MRnumber =     "1465856",
  MRreviewer =   "Yao Zhang",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Alic:1997:GAM,
  author =       "M. Ali{\'c} and P. S. Bullen and J. E.
                 Pe{\v{c}}ari{\'c} and V. Volenec",
  title =        "On the geometric--arithmetic mean inequality for
                 matrices",
  journal =      "Math. Commun.",
  volume =       "2",
  number =       "2",
  pages =        "125--128",
  year =         "1997",
  ISSN =         "1331-0623",
  MRclass =      "15A45",
  MRnumber =     "1612477",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Communications",
}

@Article{Alzer:1997:NRA,
  author =       "Horst Alzer",
  title =        "A new refinement of the arithmetic mean--geometric
                 mean inequality",
  journal =      j-ROCKY-MOUNTAIN-J-MATH,
  volume =       "27",
  number =       "3",
  pages =        "663--667",
  year =         "1997",
  CODEN =        "RMJMAE",
  DOI =          "https://doi.org/10.1216/rmjm/1181071887",
  ISSN =         "0035-7596 (print), 1945-3795 (electronic)",
  ISSN-L =       "0035-7596",
  MRclass =      "26D20",
  MRnumber =     "1490269",
  MRreviewer =   "Hrvoje {\v{S}}iki{\'c}",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Rocky Mountain Journal of Mathematics",
  journal-URL =  "http://projecteuclid.org/euclid.rmjm",
}

@Article{Ba:1997:SMA,
  author =       "Dalahu Ba",
  title =        "Some mixed arithmetic--geometric mean inequalities
                 containing parameters and their applications",
  journal =      "Neimenggu Daxue Xuebao Ziran Kexue",
  volume =       "28",
  number =       "6",
  pages =        "731--734",
  year =         "1997",
  CODEN =        "NDZKEJ",
  ISSN =         "1000-1638",
  MRclass =      "26D15",
  MRnumber =     "1620953",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Neimenggu Daxue Xuebao. Ziran Kexue. Acta Scientiarum
                 Naturalium Universitatis Neimenggu. Journal of Inner
                 Mongolia University",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@InCollection{Borwein:1997:AGMa,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:1997:PSB",
  pages =        "537--552",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Borwein:1984:AGM}.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_56",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}

@Article{Borwein:1997:AGMb,
  author =       "Jonathan A. Borwein and Petr Lison{\v{e}}k and John A.
                 Macdonald",
  title =        "Arithmetic--Geometric Means Revisited",
  journal =      j-MAPLE-TECH-NEWS,
  volume =       "4",
  number =       "1",
  pages =        "20--27",
  month =        "Winter",
  year =         "1997",
  ISSN =         "1061-5733",
  ISSN-L =       "1061-5733",
  bibdate =      "Wed Jul 23 09:11:50 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
  note =         "Special issue on Maple in the mathematical sciences.",
  URL =          "http://docserver.carma.newcastle.edu.au/4/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Maple technical newsletter",
  journal-URL =  "http://web.mit.edu/maple/www/plibrary/mtn.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}

@InCollection{Cox:1997:AGM,
  author =       "David A. Cox",
  title =        "The Arithmetic--Geometric Mean of {Gauss}",
  crossref =     "Berggren:1997:PSB",
  pages =        "481--536",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4_55",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_55",
  acknowledgement = ack-nhfb,
}

@Article{Dmitrieva:1997:FAB,
  author =       "O. M. Dmitrieva and V. N. Maloz{\"e}mov",
  title =        "On a fast algorithm based on arithmetic--geometric
                 means",
  journal =      j-ZH-VYCHISL-MAT-MAT-FIZ,
  volume =       "37",
  number =       "3",
  pages =        "277--290",
  year =         "1997",
  CODEN =        "ZVMFAN",
  ISSN =         "0044-4669",
  MRclass =      "65B99 (11Y60 33E05 65D20)",
  MRnumber =     "1452573",
  MRreviewer =   "Gh. Adam",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Zhurnal Vychislitel\cprime no{\u\i} Matematiki i
                 Matematichesko{\u\i} Fiziki. Rossi{\u\i}skaya Akademiya
                 Nauk",
  journal-URL =  "http://www.mathnet.ru/zvmmf",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Article{Dragomir:1997:SMA,
  author =       "S. S. Dragomir and D. Com{\v{a}}nescu and C. E. M.
                 Pearce",
  title =        "On some mappings associated with geometric and
                 arithmetic means",
  journal =      j-BULL-AUSTRAL-MATH-SOC,
  volume =       "55",
  number =       "2",
  pages =        "299--309",
  year =         "1997",
  CODEN =        "ALNBAB",
  DOI =          "https://doi.org/10.1017/S0004972700033967",
  ISSN =         "0004-9727 (print), 1755-1633 (electronic)",
  ISSN-L =       "0004-9727",
  MRclass =      "26D10",
  MRnumber =     "1438848",
  MRreviewer =   "Zsolt P{\'a}les",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin of the Australian Mathematical Society",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
}

@Article{Gasharov:1997:SFT,
  author =       "Vesselin Gasharov",
  title =        "Symmetric functions and the theorem of the arithmetic
                 and geometric means",
  journal =      "J. Combin. Math. Combin. Comput.",
  volume =       "25",
  pages =        "91--95",
  year =         "1997",
  ISSN =         "0835-3026",
  MRclass =      "05E05",
  MRnumber =     "1480793",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Combinatorial Mathematics and Combinatorial
                 Computing",
}

@Article{Murthy:1997:AMG,
  author =       "Amarnath Murthy",
  title =        "On the arithmetic mean geometric mean
                 inequality--another two short proofs",
  journal =      "Math. Ed. (Siwan)",
  volume =       "31",
  number =       "2",
  pages =        "118--120",
  year =         "1997",
  ISSN =         "0047-6269",
  MRclass =      "26D15",
  MRnumber =     "1463401",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematics Education",
}

@Article{Nishiwada:1997:AAG,
  author =       "Kimimasa Nishiwada",
  title =        "Algorithm of the arithmetic--geometric mean and its
                 complex limits",
  journal =      j-HOKKAIDO-MATH-J,
  volume =       "26",
  number =       "3",
  pages =        "541--564",
  year =         "1997",
  CODEN =        "HMAJDN",
  DOI =          "https://doi.org/10.14492/hokmj/1351258265",
  ISSN =         "0385-4035",
  MRclass =      "11F99 (11F06 33E05 40A05)",
  MRnumber =     "1483461",
  MRreviewer =   "D. C. Russell",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Hokkaido Mathematical Journal",
  journal-URL =  "http://projecteuclid.org/hokmj",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@InCollection{Pecaric:1997:AMG,
  author =       "J. Pe{\v{c}}ari{\'c} and B. Mond",
  booktitle =    "General inequalities, 7 ({Oberwolfach}, 1995)",
  title =        "The arithmetic mean---the geometric mean and related
                 matrix inequalities",
  volume =       "123",
  publisher =    "Birkh{\"a}user, Basel",
  pages =        "77--91",
  year =         "1997",
  MRclass =      "15A45 (26D15 47A63)",
  MRnumber =     "1457271",
  MRreviewer =   "I. Gavrea",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "Internat. Ser. Numer. Math.",
  acknowledgement = ack-nhfb,
}

@Article{Pecaric:1997:NPA,
  author =       "Josip Pe{\v{c}}ari{\'c} and Sanja Varo{\v{s}}anec",
  title =        "A new proof of the arithmetic mean---the geometric
                 mean inequality",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "215",
  number =       "2",
  pages =        "577--578",
  year =         "1997",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1006/jmaa.1997.5616",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "26D15",
  MRnumber =     "1490770",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
}

@InCollection{Salamin:1997:CUA,
  author =       "Eugene Salamin",
  title =        "Computation of $ \pi $ Using Arithmetic--Geometric
                 Mean",
  crossref =     "Berggren:1997:PSB",
  pages =        "418--423",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4_46",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_46",
  acknowledgement = ack-nhfb,
}

@Article{Seiffert:1997:TIA,
  author =       "H. J. Seiffert",
  title =        "Three inequalities for the arithmetic, identric, and
                 geometric means",
  journal =      j-SIAM-REVIEW,
  volume =       "39",
  number =       "2",
  pages =        "330--332",
  month =        "????",
  year =         "1997",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "June 1997",
  xxnote =       "Check title word: identric??",
}

@Article{Bencze:1998:NPA,
  author =       "Mih{\'a}ly Bencze",
  title =        "A new proof of the arithmetic--geometric mean
                 inequality",
  journal =      j-OCTOGON-MATH-MAG,
  volume =       "6",
  number =       "1",
  pages =        "49--50",
  year =         "1998",
  ISSN =         "1222-5657 (print), 2248-1893 (electronic)",
  MRclass =      "26D15",
  MRnumber =     "1630953",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Octogon Mathematical Magazine",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Book{Borwein:1998:PAS,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "Pi and the {AGM}: A study in analytic number theory
                 and computational complexity",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xvi + 414",
  year =         "1998",
  ISBN =         "0-471-31515-X",
  ISBN-13 =      "978-0-471-31515-5",
  MRclass =      "11Y60 (11B65 68Q25)",
  MRnumber =     "1641658",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Reprint of the 1987 original.",
  series =       "Canadian Mathematical Society Series of Monographs and
                 Advanced Texts, 4",
  acknowledgement = ack-nhfb,
}

@Article{Dragomir:1998:IAG,
  author =       "Sever S. Dragomir",
  title =        "The improvement of arithmetic--geometric inequality
                 for weighted means",
  journal =      "Ranchi Univ. Math. J.",
  volume =       "29",
  pages =        "11--19 (1999)",
  year =         "1998",
  ISSN =         "0079-9602",
  MRclass =      "26D15",
  MRnumber =     "1755103",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Ranchi University Mathematical Journal",
}

@InCollection{Kanas:1998:UCC,
  author =       "S. Kanas and A. Lecko",
  booktitle =    "Transform methods \& special functions, {Varna} '96",
  title =        "Univalence criteria connected with arithmetic and
                 geometric means. {I}",
  publisher =    "Bulgarian Acad. Sci., Sofia",
  pages =        "201--209",
  year =         "1998",
  MRclass =      "30C80",
  MRnumber =     "1667743",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kosaki:1998:AGM,
  author =       "Hideki Kosaki",
  title =        "Arithmetic--Geometric Mean and Related Inequalities
                 for Operators",
  journal =      j-J-FUNCT-ANAL,
  volume =       "156",
  number =       "2",
  pages =        "429--451",
  year =         "1998",
  CODEN =        "JFUAAW",
  DOI =          "https://doi.org/10.1006/jfan.1998.3258",
  ISSN =         "0022-1236 (print), 1096-0783 (electronic)",
  ISSN-L =       "0022-1236",
  MRclass =      "47A63 (47A30)",
  MRnumber =     "1636964",
  MRreviewer =   "Takayuki Furuta",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S002212369893258X",
  abstract =     "In recent years certain arithmetic--geometric mean and
                 related inequalities for operators and unitarily
                 invariant norms have been obtained by many authors
                 based on majorization technique and so on. We first
                 point out that they are direct consequences of integral
                 expressions of relevant operators. Furthermore we
                 obtain related new inequalities (Theorems 4, 5, and 6)
                 based on our current approach.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Functional Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00221236",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Article{Maligranda:1998:WHI,
  author =       "Lech Maligranda",
  title =        "Why {H{\"o}lder's Inequality} should be called
                 {Rogers' Inequality}",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "1",
  number =       "1",
  pages =        "69--83",
  month =        "????",
  year =         "1998",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  ISSN-L =       "1331-4343",
  bibdate =      "Fri Feb 15 16:18:07 2013",
  bibsource =    "http://mia.ele-math.com/;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  ZMnumber =     "0889.26001",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Inequal. Appl.",
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
  keywords =     "H{\"o}lder inequality; Cauchy inequality; Jensen
                 inequality; history; biographies",
  ZMclass =      "26-03 (Historical (real functions)); 26D15
                 (Inequalities for sums, series and integrals of real
                 functions); 01A50 (Mathematics in the 18th century);
                 01A60 (Mathematics in the 20th century); 01A70
                 (Biographies, obituaries, personalia, bibliographies)",
  ZMreviewer =   "Johann Acz{\'e}l (Waterloo/Ontario)",
}

@Article{Sole:1998:LCA,
  author =       "P. Sol{\'e} and P. Loyer",
  title =        "{$ U_n $} Lattices, Construction {$B$}, and {AGM}
                 Iterations",
  journal =      j-EUR-J-COMB,
  volume =       "19",
  number =       "2",
  pages =        "227--236",
  month =        feb,
  year =         "1998",
  CODEN =        "EJOCDI",
  DOI =          "https://doi.org/10.1006/eujc.1997.0185",
  ISSN =         "0195-6698 (print), 1095-9971 (electronic)",
  ISSN-L =       "0195-6698",
  bibdate =      "Tue Mar 14 17:10:52 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "European Journal of Combinatorics",
}

@Article{Toader:1998:SMV,
  author =       "Gh. Toader",
  title =        "Some Mean Values Related to the Arithmetic--Geometric
                 Mean",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "218",
  number =       "2",
  pages =        "358--368",
  year =         "1998",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1006/jmaa.1997.5766",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "26D15 (39B22)",
  MRnumber =     "1606799",
  MRreviewer =   "Zsolt P{\'a}les",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X97957668",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Article{Alzer:1999:SIA,
  author =       "Horst Alzer",
  title =        "Some inequalities for arithmetic and geometric means",
  journal =      j-PROC-R-SOC-EDINB-SECT-A-MATH,
  volume =       "129",
  number =       "2",
  pages =        "221--228",
  year =         "1999",
  CODEN =        "PEAMDU",
  DOI =          "https://doi.org/10.1017/S0308210500021326",
  ISSN =         "0308-2105 (print), 1473-7124 (electronic)",
  ISSN-L =       "0308-2105",
  MRclass =      "26D15",
  MRnumber =     "1686698",
  MRreviewer =   "Wolfram Koepf",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society of Edinburgh. Section
                 A. Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PRM",
}

@TechReport{Boldo:1999:CRE,
  author =       "Sylvie Boldo",
  title =        "Calcul rapide et exact de fonctions
                 {\'e}l{\'e}mentaires en pr{\'e}cision arbitraire par la
                 moyenne arithm{\'e}tico-g{\'e}om{\'e}trique. ({French})
                 [Rapid and exact computation of elementary functions in
                 arbitrary precision by the arithmetic--geometric
                 mean]",
  type =         "Report",
  institution =  "INRIA, Projet Spaces, LORIA, Campus Scientifique",
  address =      "B.P. 239, 54506 Vandoeuvre-l{\`e}s-Nancy Cedex,
                 France",
  pages =        "29",
  year =         "1999",
  bibdate =      "Tue Nov 23 11:00:03 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Under the direction of Paul Zimmermann.",
  URL =          "http://perso.ens-lyon.fr/sylvie.boldo/doc/mpfr.ps",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Article{Cass:1999:BRP,
  author =       "Peter Cass",
  title =        "Book Review: {{\booktitle{Pi and the AGM}}}",
  journal =      j-MATH-GAZ,
  volume =       "83",
  number =       "497",
  pages =        "334--335",
  month =        jul,
  year =         "1999",
  CODEN =        "MAGAAS",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Sat Aug 13 18:09:13 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/3619084",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}

@Article{Donagi:1999:AGM,
  author =       "Ron Donagi and Ron Livn{\'e}",
  title =        "The arithmetic--geometric mean and isogenies for
                 curves of higher genus",
  journal =      j-ANN-SC-NORM-SUPER-PISA-CL-SCI,
  volume =       "28",
  number =       "2",
  pages =        "323--339",
  year =         "1999",
  CODEN =        "PSNAAI",
  ISSN =         "0391-173x (print), 2036-2145 (electronic)",
  ISSN-L =       "0391-173X",
  MRclass =      "14H40 (14K02)",
  MRnumber =     "1736231",
  MRreviewer =   "Arnaud Beauville",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.numdam.org/item?id=ASNSP_1999_4_28_2_323_0",
  acknowledgement = ack-nhfb,
  fjournal =     "Annali della Scuola Normale Superiore di Pisa. Classe
                 di Scienze. Serie IV",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Article{Dragomir:1999:CAM,
  author =       "S. S. Dragomir",
  title =        "Counterparts of arithmetic mean--geometric
                 mean--harmonic mean inequality",
  journal =      "Studia Univ. Babe{\c{s}}-Bolyai Math.",
  volume =       "44",
  number =       "4",
  pages =        "37--42",
  year =         "1999",
  ISSN =         "0252-1938",
  MRclass =      "26D15",
  MRnumber =     "1989064",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Universitatis Babe{\c{s}}-Bolyai. Studia.
                 Mathematica",
}

@Article{Fournier:1999:EGA,
  author =       "Richard Fournier",
  title =        "Extensions of the geometric--arithmetic means
                 inequality to a disc of the complex plane",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "2",
  number =       "1",
  pages =        "19--24",
  year =         "1999",
  DOI =          "https://doi.org/10.7153/mia-02-03",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "30C45 (26D15)",
  MRnumber =     "1667789",
  MRreviewer =   "Wolfram Koepf",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Hiai:1999:CVM,
  author =       "Fumio Hiai and Hideki Kosaki",
  title =        "Comparison of Various Means for Operators",
  journal =      j-J-FUNCT-ANAL,
  volume =       "163",
  number =       "2",
  pages =        "300--323",
  year =         "1999",
  CODEN =        "JFUAAW",
  DOI =          "https://doi.org/10.1006/jfan.1998.3375",
  ISSN =         "0022-1236 (print), 1096-0783 (electronic)",
  ISSN-L =       "0022-1236",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022123698933754",
  abstract =     "For Hilbert space operators $H$, $K$, $X$ with $ H, K
                 \geq 0$ the norm inequality $ |||H^{1 / 2} X K^{1 /
                 2}||| \leq (1 / 2) |||H X + X K|||$ is known, where |||
                 \cdot ||| is an arbitrary unitarily invariant norm. A
                 refinement of this arithmetic--geometric mean
                 inequality is studied. Similar norm inequalities are
                 indeed established for various natural means for
                 operators such as the logarithmic mean.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of functional analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00221236",
}

@Article{Joseph:1999:AMG,
  author =       "James E. Joseph and Myung H. Kwack",
  title =        "The arithmetic-mean--geometric-mean inequality derived
                 from closed polynomial functions",
  journal =      "Missouri J. Math. Sci.",
  volume =       "11",
  number =       "2",
  pages =        "103--106",
  year =         "1999",
  ISSN =         "0899-6180",
  MRclass =      "26D15",
  MRnumber =     "1694273",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Missouri Journal of Mathematical Sciences",
}

@Article{Kittaneh:1999:SNI,
  author =       "Fuad Kittaneh",
  title =        "Some norm inequalities for operators",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "87--96",
  month =        mar,
  year =         "1999",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-1999-010-6",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "47A30, 47B10, 47B15, 47B20",
  bibdate =      "Thu Sep 8 10:22:25 MDT 2011",
  bibsource =    "http://cms.math.ca/cmb/v42/;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/canmathbull.bib",
  abstract =     "Let $ A_i $, $ B_i $ and $ X_i $ $ (i = 1, 2, \dots,
                 n) $ be operators on a separable Hilbert space. It is
                 shown that if $f$ and $g$ are nonnegative continuous
                 functions on $ [0, \infty)$ which satisfy the relation
                 $ f(t)g(t) = t$ for all $t$ in $ [0, \infty)$, then $$
                 \Biglvert \, \Bigl | \sum^n_{i = 1} A^*_i X_i B_i \Bigr
                 |^r \, \Bigrvert^2 \leq \Biglvert \Bigl (\sum^n_{i = 1}
                 A^*_i f (|X^*_i|)^2 A_i \Bigr)^r \Bigrvert \, \Biglvert
                 \Bigl (\sum^n_{i = 1} B^*_i g (|X_i|)^2 B_i \Bigr)^r
                 \Bigrvert $$ for every $ r > 0$ and for every unitarily
                 invariant norm. This result improves some known
                 Cauchy--Schwarz type inequalities. Norm inequalities
                 related to the arithmetic--geometric mean inequality
                 and the classical Heinz inequalities are also
                 obtained.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "47A30, 47B10, 47B15, 47B20",
  fjournal =     "Canadian Mathematical Bulletin. Bulletin Canadien de
                 Math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
  journalabbrev = "CMB",
  keywords =     "arithmetic--geometric mean inequality; Cauchy--Schwarz
                 inequality; Heinz inequality; positive operator;
                 Unitarily invariant norm",
  refnum =       "7284",
}

@InCollection{Latala:1999:EBG,
  author =       "Rafa{\l} Lata{\l}a",
  booktitle =    "Convex geometric analysis ({Berkeley}, {CA}, 1996)",
  title =        "On the equivalence between geometric and arithmetic
                 means for log-concave measures",
  volume =       "34",
  publisher =    "Cambridge Univ. Press, Cambridge",
  pages =        "123--127",
  year =         "1999",
  DOI =          "https://doi.org/10.2977/prims/1195144757",
  MRclass =      "60E15 (60B11)",
  MRnumber =     "1665584",
  MRreviewer =   "Pawel Hitczenko",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "Math. Sci. Res. Inst. Publ.",
  acknowledgement = ack-nhfb,
}

@Article{Sampedro:1999:DIP,
  author =       "J. Cruz Sampedro and M. Tetlalmatzi Montiel",
  title =        "A direct inductive proof of the geometric
                 mean--arithmetic mean inequality",
  journal =      "Miscel{\'a}nea Mat.",
  volume =       "28",
  pages =        "11--15",
  year =         "1999",
  ISSN =         "1665-5478",
  MRclass =      "26D15",
  MRnumber =     "1823254",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Miscel{\'a}nea Matem{\'a}tica",
}

@Article{Sandor:1999:AGM,
  author =       "J{\'o}zsef S{\'a}ndor",
  title =        "On the arithmetic--geometric mean of {Gauss}",
  journal =      j-OCTOGON-MATH-MAG,
  volume =       "7",
  number =       "1",
  pages =        "108--115",
  year =         "1999",
  ISSN =         "1222-5657 (print), 2248-1893 (electronic)",
  MRclass =      "26D15",
  MRnumber =     "1730039",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Octogon Mathematical Magazine",
  zzbibdate =    "Tue Aug 15 10:35:36 2017",
}

@Article{Wang:1999:SLT,
  author =       "Liqiu Wang",
  title =        "Second law of thermodynamics and
                 arithmetic-mean--geometric-mean inequality",
  journal =      "Internat. J. Modern Phys. B",
  volume =       "13",
  number =       "21-22",
  pages =        "2791--2793",
  year =         "1999",
  DOI =          "https://doi.org/10.1142/S0217979299002678",
  ISSN =         "0217-9792 (print), 1793-6578 (electronic)",
  MRclass =      "80A10 (26D15)",
  MRnumber =     "1713415",
  bibdate =      "Tue Aug 15 10:35:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Modern Physics B",
}

@Article{Alsina:2000:PWA,
  author =       "Claudi Alsina",
  title =        "Proof without Words: The Arithmetic--Geometric Mean
                 Inequality for Three Positive Numbers",
  journal =      j-MATH-MAG,
  volume =       "73",
  number =       "2",
  pages =        "97",
  year =         "2000",
  CODEN =        "MAMGA8",
  ISSN =         "0025-570X",
  MRnumber =     "1573443",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/2691079?origin=pubexport",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}

@Article{Bhatia:2000:NMA,
  author =       "Rajendra Bhatia and Fuad Kittaneh",
  title =        "Notes on matrix arithmetic--geometric mean
                 inequalities",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "308",
  number =       "1--3",
  pages =        "203--211",
  day =          "15",
  month =        mar,
  year =         "2000",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/S0024-3795(00)00048-3",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A45 (15A42 15A60 47A30)",
  MRnumber =     "1751140",
  MRreviewer =   "Yao Zhang",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2000.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/30/19/125/25/36/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/30/19/125/25/36/article.pdf;
                 http://www.sciencedirect.com/science/article/pii/S0024379500000483",
  abstract =     "For positive semi-definite $ n \times n $ matrices,
                 the inequality $ 4 ||| A B ||| \leq ||| (A + B)^2 ||| $
                 is shown to hold for every unitarily invariant norm.
                 The connection of this with some other matrix
                 arithmetic--geometric mean inequalities and trace
                 inequalities is discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Arithmetic--geometric mean; Majorisation; Singular
                 values; Unitarily invariant norms",
}

@InCollection{Borwein:2000:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:2000:PSB",
  pages =        "537--552",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4757-3240-5_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Borwein:1984:AGM}.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_56",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}

@InCollection{Cox:2000:AGM,
  author =       "David A. Cox",
  title =        "The Arithmetic--Geometric Mean of {Gauss}",
  crossref =     "Berggren:2000:PSB",
  pages =        "481--536",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4757-3240-5_55",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_55",
  acknowledgement = ack-nhfb,
}

@Article{Hao:2000:CIA,
  author =       "Zhi Chuan Hao",
  title =        "A combinatorial inequality for the arithmetic and
                 geometric means",
  journal =      "Guizhou Shifan Daxue Xuebao Ziran Kexue Ban",
  volume =       "18",
  number =       "1",
  pages =        "28--31",
  year =         "2000",
  ISSN =         "1004-5570",
  MRclass =      "26D15",
  MRnumber =     "1748759",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Guizhou Shifan Daxue Xuebao. Ziran Kexue Ban. Journal
                 of Guizhou Normal University. Natural Sciences",
}

@InCollection{Kwon:2000:AGM,
  author =       "Ern Gun Kwon and Kwang Ho Shon",
  booktitle =    "Finite or infinite dimensional complex analysis
                 ({Fukuoka}, 1999)",
  title =        "On the arithmetic--geometric mean inequality",
  volume =       "214",
  publisher =    "Dekker, New York",
  pages =        "233--235",
  year =         "2000",
  MRclass =      "26D15",
  MRnumber =     "1771322",
  MRreviewer =   "L. Losonczi",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "Lecture Notes in Pure and Appl. Math.",
  acknowledgement = ack-nhfb,
}

@Article{Kwon:2000:ATB,
  author =       "E. G. Kwon and S. T. Lee and K. H. Shon",
  title =        "An additional term between arithmetic mean and
                 geometric mean",
  journal =      "Bull. Korean Math. Soc.",
  volume =       "37",
  number =       "2",
  pages =        "285--289",
  year =         "2000",
  ISSN =         "1015-8634",
  MRclass =      "26D15 (28A35)",
  MRnumber =     "1757495",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin of the Korean Mathematical Society",
}

@InCollection{Salamin:2000:CUA,
  author =       "Eugene Salamin",
  title =        "Computation of $ \pi $ Using Arithmetic--Geometric
                 Mean",
  crossref =     "Berggren:2000:PSB",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "418--423",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4757-3240-5_46",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_46",
  acknowledgement = ack-nhfb,
}

@Article{Sury:2000:AGM,
  author =       "B. Sury",
  title =        "The arithmetico--geometric mean of {Gauss}: How to
                 find the perimeter of an ellipse",
  journal =      j-RESONANCE,
  volume =       "5",
  number =       "8",
  pages =        "72--83",
  month =        aug,
  year =         "2000",
  CODEN =        "RESOFE",
  DOI =          "https://doi.org/10.1007/bf02837938",
  ISSN =         "0971-8044 (print), 0973-712X (electronic)",
  bibdate =      "Tue Mar 14 15:45:02 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Resonance",
  journal-URL =  "http://link.springer.com/journal/12045",
}

@Article{Wachspress:2000:EEF,
  author =       "E. L. Wachspress",
  title =        "Evaluating elliptic functions and their inverses",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "39",
  number =       "3--4",
  pages =        "131--136",
  month =        feb,
  year =         "2000",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/S0898-1221(99)00339-9",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122199003399",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "arithmetic--geometric mean (AGM)",
}

@Article{Yang:2000:AGM,
  author =       "Ling Ou Yang",
  title =        "Arithmetic--geometric mean inequalities for trace of
                 operators",
  journal =      "Math. Theory Appl. (Changsha)",
  volume =       "20",
  number =       "3",
  pages =        "117--120",
  year =         "2000",
  ISSN =         "1006-8074",
  MRclass =      "47A64 (47A63)",
  MRnumber =     "1806708",
  MRreviewer =   "Frank Hansen",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Theory and Applications",
}

@Article{Bracken:2001:AGM,
  author =       "Paul Bracken",
  title =        "An arithmetic--geometric mean inequality",
  journal =      j-EXPO-MATH,
  volume =       "19",
  number =       "3",
  pages =        "273--279",
  year =         "2001",
  DOI =          "https://doi.org/10.1016/S0723-0869(01)80006-2",
  ISSN =         "0723-0869 (print), 1878-0792 (electronic)",
  ISSN-L =       "0723-0869",
  MRclass =      "26D15",
  MRnumber =     "1852077",
  MRreviewer =   "Antal Bege",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0723086901800062",
  abstract =     "Several integrals which are related to the
                 arithmetic--geometric mean are developed and proved in
                 a very elementary way. These results can be used to
                 prove a known inequality which relates this mean to the
                 logarithmic mean.",
  acknowledgement = ack-nhfb,
  fjournal =     "Expositiones Mathematicae",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07230869",
}

@Article{Dobbs:2001:PAG,
  author =       "David E. Dobbs",
  title =        "A proof of the arithmetic--geometric mean inequality
                 using non-{Euclidean} geometry",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "32",
  number =       "5",
  pages =        "778--782",
  year =         "2001",
  CODEN =        "IJMEBM",
  DOI =          "https://doi.org/10.1080/002073901753124655",
  ISSN =         "0020-739x (print), 1464-5211 (electronic)",
  ISSN-L =       "0020-739X",
  MRclass =      "26D15 (51M10)",
  MRnumber =     "1862675",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  journal-URL =  "http://www.tandfonline.com/loi/tmes20",
}

@Article{Ekart:2001:NGA,
  author =       "Anik{\'o} Ek{\'a}rt and S. Z. N{\'e}meth",
  title =        "A noncontinuous generalization of the
                 arithmetic--geometric mean",
  journal =      j-APPL-MATH-COMP,
  volume =       "124",
  number =       "2",
  pages =        "261--279",
  day =          "25",
  month =        oct,
  year =         "2001",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/S0096-3003(00)00098-9",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "40A05",
  MRnumber =     "1857690",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.elsevier.com/locate/issn/00963003;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib",
  URL =          "http://www.elsevier.com/gej-ng/10/9/12/113/31/36/abstract.html;
                 http://www.sciencedirect.com/science/article/pii/S0096300300000989",
  abstract =     "The notions of prickly set, scalar and vectorial mean
                 are defined. A noncontinuous generalization of the
                 arithmetic--geometric mean is given, by considering the
                 recursion xn+1=F(xn), where F:C \to C is a vectorial
                 mean and C is a closed prickly subset of Rm. The
                 convergence of this recursion is proved and it is shown
                 that the limit is contained in the diagonal of C. If F
                 is continuous, it is deduced that the limit of the
                 recursion is a continuous function of the initial value
                 x=x0. Denoting the limit by F\infty(x) it is proved
                 that if F is monotone, then F\infty it is also monotone
                 (where the monotonicity is considered with respect to
                 the closed cone R+m).",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "Arithmetic--geometric mean; F-mean; Prickly set;
                 Scalar mean; Vectorial mean",
}

@Article{Nakamura:2001:AAA,
  author =       "Yoshimasa Nakamura",
  title =        "Algorithms associated with arithmetic, geometric and
                 harmonic means and integrable systems",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "131",
  number =       "1--2",
  pages =        "161--174",
  day =          "1",
  month =        jun,
  year =         "2001",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00316-2",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65P40 (37N30 39A10)",
  MRnumber =     "1835710",
  bibdate =      "Sat Feb 25 12:45:18 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700003162",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Sury:2001:LA,
  author =       "B. Sury",
  title =        "Logarithm and {AGM}",
  journal =      j-RESONANCE,
  volume =       "6",
  number =       "11",
  pages =        "85--86",
  month =        nov,
  year =         "2001",
  CODEN =        "RESOFE",
  DOI =          "https://doi.org/10.1007/bf02868248",
  ISSN =         "0971-8044 (print), 0973-712X (electronic)",
  bibdate =      "Tue Mar 14 15:35:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Resonance",
  journal-URL =  "http://link.springer.com/journal/12045",
}

@Article{Yang:2001:AGM,
  author =       "Hansheng Yang and Heng Yang",
  title =        "The Arithmetic--Geometric Mean Inequality and the
                 Constant $e$",
  journal =      j-MATH-MAG,
  volume =       "74",
  number =       "4",
  pages =        "321--323",
  year =         "2001",
  CODEN =        "MAMGA8",
  ISSN =         "0025-570X",
  MRnumber =     "1573553",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/2691107?origin=pubexport",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}

@Article{Alzer:2002:AMG,
  author =       "Horst Alzer and Stephan Ruscheweyh",
  title =        "The arithmetic mean--geometric mean inequality for
                 complex numbers",
  journal =      "Analysis (Munich)",
  volume =       "22",
  number =       "3",
  pages =        "277--283",
  year =         "2002",
  DOI =          "https://doi.org/10.1524/anly.2002.22.3.277",
  ISSN =         "0174-4747",
  MRclass =      "30A10 (26E60)",
  MRnumber =     "1938378",
  MRreviewer =   "Arcadii Z. Grinshpan",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Analysis. International Mathematical Journal of
                 Analysis and its Applications",
}

@Article{Charzynski:2002:IBA,
  author =       "Zygmunt Karol Charzy{\'n}ski",
  title =        "On an inequality between an arithmetic mean and a
                 geometric mean",
  journal =      "Zeszyty Nauk. Politech. Rzeszowskiej Mat.",
  volume =       "26",
  pages =        "165--171",
  year =         "2002",
  ISSN =         "1232-7867",
  MRclass =      "26D15 (26E60)",
  MRnumber =     "1949601",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Zeszyty Naukowe Politechniki Rzeszowskiej.
                 Matematyka",
}

@Article{Disch:2002:CPV,
  author =       "Burkhard Disch",
  title =        "Computing present values by the {AGM}",
  journal =      "{Bl{\"a}tter der DGVFM}",
  volume =       "25",
  number =       "4",
  pages =        "831--849",
  month =        oct,
  year =         "2002",
  DOI =          "https://doi.org/10.1007/bf02809119",
  bibdate =      "Tue Mar 14 15:31:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Gaudry:2002:CCS,
  author =       "Pierrick Gaudry",
  booktitle =    "{International Conference on the Theory and
                 Application of Cryptology and Information Security:
                 ASIACRYPT 2002: Advances in Cryptology --- ASIACRYPT
                 2002}",
  title =        "A Comparison and a Combination of {SST} and {AGM}
                 Algorithms for Counting Points of Elliptic Curves in
                 Characteristic $2$",
  volume =       "2501",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "311--327",
  year =         "2002",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/3-540-36178-2_20",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Mar 14 15:33:17 2017",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2501.htm;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2002e.bib",
  series =       "Lecture Notes in Computer Science",
  URL =          "http://link.springer.de/link/service/series/0558/bibs/2501/25010311.htm;
                 http://link.springer.de/link/service/series/0558/papers/2501/25010311.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Georgakis:2002:IAG,
  author =       "Constantine Georgakis",
  title =        "On the inequality for the arithmetic and geometric
                 means",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "5",
  number =       "2",
  pages =        "215--218",
  year =         "2002",
  DOI =          "https://doi.org/10.7153/mia-05-23",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "26D15",
  MRnumber =     "1899088",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Xie:2002:SGA,
  author =       "Ziqing Xie",
  title =        "On the Summation of Generalized Arithmetic--Geometric
                 Trigonometric Series",
  journal =      j-FIB-QUART,
  volume =       "40",
  number =       "2",
  pages =        "128--135",
  month =        may,
  year =         "2002",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:03:33 MDT 2011",
  bibsource =    "http://www.fq.math.ca/40-2.html;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/40-2/xie.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Unpublished{Borwein:2003:ACFa,
  author =       "Jonathan M. Borwein",
  title =        "The {AGM} Continued Fraction of {Ramanujan}",
  day =          "31",
  month =        jul,
  year =         "2003",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "CECM Day 2003, Simon Fraser University, Burnaby, BC,
                 Canada.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:2003:ACFb,
  author =       "Jonathan M. Borwein",
  title =        "The {AGM} Continued Fraction of {Ramanujan}",
  day =          "16",
  month =        sep,
  year =         "2003",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "First Plenary Lecture, First Congress of the
                 Mathematical Society of South East Europe (MASSE{\'E}),
                 Borovets, Bulgaria.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:2003:ACFc,
  author =       "Jonathan M. Borwein",
  title =        "The {AGM} Continued Fraction of {Ramanujan}",
  day =          "14",
  month =        oct,
  year =         "2003",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, Reed College, OR, USA.",
  acknowledgement = ack-nhfb,
}

@Article{Gluskin:2003:NGA,
  author =       "E. Gluskin and V. Milman",
  title =        "Note on the Geometric--Arithmetic Mean Inequality",
  journal =      j-LECT-NOTES-MATH,
  volume =       "1807",
  pages =        "131--135",
  year =         "2003",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/978-3-540-36428-3_11",
  ISBN =         "3-540-00485-8 (print), 3-540-36428-5 (e-book)",
  ISBN-13 =      "978-3-540-00485-1 (print), 978-3-540-36428-3
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  MRclass =      "46B20 (46B09)",
  MRnumber =     "2083393",
  MRreviewer =   "Niels J\o rgen Nielsen",
  bibdate =      "Fri May 9 19:07:18 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm2000.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-540-36428-3_11/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/b10415",
  book-URL =     "http://www.springerlink.com/content/978-3-540-36428-3",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
  xxpages =      "130--135",
}

@Article{Guo:2003:IMR,
  author =       "Bai-Ni Guo and Feng Qi",
  title =        "Inequalities and monotonicity of the ratio for the
                 geometric means of a positive arithmetic sequence with
                 arbitrary difference",
  journal =      j-TAMKANG-J-MATH,
  volume =       "34",
  number =       "3",
  pages =        "261--270",
  year =         "2003",
  ISSN =         "0049-2930 (print), 2073-9826 (electronic)",
  ISSN-L =       "2073-9826",
  MRclass =      "26D07 (26A48 26D15 26E60)",
  MRnumber =     "2001922",
  MRreviewer =   "Attila Gil{\'a}nyi",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tamkang Journal of Mathematics",
  journal-URL =  "http://journals.math.tku.edu.tw/index.php/TKJM",
}

@Article{Katsuura:2003:GAG,
  author =       "Hidefumi Katsuura",
  title =        "Generalizations of the Arithmetic--Geometric Mean
                 Inequality and a Three Dimensional Puzzle",
  journal =      j-COLLEGE-MATH-J,
  volume =       "34",
  number =       "4",
  pages =        "280--282",
  month =        sep,
  year =         "2003",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.2003.11922018",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:53:32 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/07468342.2003.11922018",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  onlinedate =   "30 Jan 2018",
}

@Article{Knockaert:2003:BUB,
  author =       "Luc Knockaert",
  title =        "Best upper bounds based on the arithmetic--geometric
                 mean inequality",
  journal =      j-ARCH-INEQUAL-APPL,
  volume =       "1",
  number =       "1",
  pages =        "85--90",
  year =         "2003",
  ISSN =         "1542-6149",
  MRclass =      "15A42 (15A12 60E15)",
  MRnumber =     "1992268",
  MRreviewer =   "E. Seneta",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Archives of Inequalities and Applications. An
                 International Journal for Theory and Applications",
}

@Article{Mercer:2003:RAG,
  author =       "Peter R. Mercer",
  title =        "Refined arithmetic, geometric and harmonic mean
                 inequalities",
  journal =      j-ROCKY-MOUNTAIN-J-MATH,
  volume =       "33",
  number =       "4",
  pages =        "1459--1464",
  year =         "2003",
  CODEN =        "RMJMAE",
  DOI =          "https://doi.org/10.1216/rmjm/1181075474",
  ISSN =         "0035-7596 (print), 1945-3795 (electronic)",
  ISSN-L =       "0035-7596",
  MRclass =      "26D15 (26E60)",
  MRnumber =     "2052499",
  MRreviewer =   "J. Horv{\'a}th",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Rocky Mountain Journal of Mathematics",
  journal-URL =  "http://projecteuclid.org/euclid.rmjm",
}

@Article{Monhor:2003:AGM,
  author =       "D. Monhor",
  title =        "The arithmetic--geometric mean and the elliptic mean
                 error",
  journal =      j-ACTA-GEOD-GEOPHYS-HU,
  volume =       "38",
  number =       "1",
  pages =        "??--??",
  month =        feb,
  year =         "2003",
  CODEN =        "AGGHFW",
  DOI =          "https://doi.org/10.1556/AGeod.38.2003.1.8",
  ISSN =         "1217-8977 (print), 1587-1037 (electronic)",
  ISSN-L =       "1217-8977",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/article/10.1556/AGeod.38.2003.1.8",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Geodaetica et Geophysica Hungarica",
  journal-URL =  "http://www.akademiai.com/loi/074",
  remark =       "Journal archive contains only years 2001 to date.",
}

@Article{Qi:2003:IMRa,
  author =       "Feng Qi",
  title =        "Inequalities and monotonicity of the ratio for the
                 geometric means of a positive arithmetic sequence with
                 unit difference",
  journal =      j-AUSTRALIAN-MATH-SOC-GAZ,
  volume =       "30",
  number =       "3",
  pages =        "142--147",
  year =         "2003",
  ISSN =         "0311-0729 (print), 1326-2297 (electronic)",
  ISSN-L =       "0311-0729",
  MRclass =      "26D07 (26E60)",
  MRnumber =     "1988519",
  MRreviewer =   "Attila Gil{\'a}nyi",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Australian Mathematical Society. Gazette",
  journal-URL =  "http://www.austms.org.au/gazette",
}

@Article{Qi:2003:IMRb,
  author =       "Feng Qi",
  title =        "Inequalities and monotonicity of the ratio of the
                 geometric means of a positive arithmetic sequence with
                 unit difference",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "34",
  number =       "4",
  pages =        "601--607",
  year =         "2003",
  CODEN =        "IJMEBM",
  DOI =          "https://doi.org/10.1080/0020739031000149010",
  ISSN =         "0020-739x (print), 1464-5211 (electronic)",
  ISSN-L =       "0020-739X",
  MRclass =      "11B75 (11B25 26D15)",
  MRnumber =     "1998815",
  MRreviewer =   "Shiro Ando",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  journal-URL =  "http://www.tandfonline.com/loi/tmes20",
}

@Article{Rooin:2003:AIB,
  author =       "Jamal Rooin",
  title =        "{AGM} inequality with binomial expansion",
  journal =      j-ELEM-MATH,
  volume =       "58",
  number =       "3",
  pages =        "115--117",
  month =        aug,
  year =         "2003",
  DOI =          "https://doi.org/10.1007/s00017-003-0188-x",
  ISSN =         "0013-6018 (print), 1420-8962 (electronic)",
  ISSN-L =       "0013-6018",
  bibdate =      "Tue Mar 14 15:30:54 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elemente der Mathematik",
}

@Article{Roy:2003:CBW,
  author =       "Dilip Roy",
  title =        "Characterization of a bivariate {Weibull} distribution
                 based on arithmetic, geometric and harmonic means of
                 failure rates",
  journal =      "J. Appl. Statist. Sci.",
  volume =       "12",
  number =       "3",
  pages =        "191--199",
  year =         "2003",
  ISSN =         "1067-5817",
  MRclass =      "62N05 (62E10 62H05)",
  MRnumber =     "2038808",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistical Science",
}

@Misc{Tkachev:2003:EFI,
  author =       "Vladimir G. Tkachev",
  title =        "Elliptic functions: Introduction course",
  howpublished = "Web lecture notes.",
  day =          "25",
  month =        nov,
  year =         "2003",
  bibdate =      "Wed Mar 15 08:43:21 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://users.mai.liu.se/vlatk48/teaching/lect2-agm.pdf",
  acknowledgement = ack-nhfb,
  tableofcontents = "Chapter 1. Elliptic integrals and Jacobi's theta
                 functions / 5 \\
                 1.1. Elliptic integrals and the AGM: real case / 5 \\
                 1.1.3. The arithmetic--geometric mean iteration / 7 \\
                 1.2. Lemniscates and elastic curves / 11 \\
                 1.3. Euler's addition theorem / 18 \\
                 1.4. Theta functions: preliminaries 5 / 24 \\
                 Chapter 2. General theory of doubly periodic functions
                 / 31 \\
                 2.1. Preliminaries / 31 \\
                 2.2. Periods of analytic functions / 33 \\
                 2.3. Existence of doubly periodic functions / 36 \\
                 2.4. Liouville's theorems / 38 \\
                 2.5. The Weierstrass function $\wp(z)$ / 43 \\
                 2.6. Modular forms / 51 \\
                 Bibliography / 61",
}

@InCollection{Borwein:2004:AGMa,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:2004:PSB",
  pages =        "537--552",
  year =         "2004",
  DOI =          "https://doi.org/10.1007/978-1-4757-4217-6_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Borwein:1984:AGM}.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_56",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}

@Unpublished{Borwein:2004:RACa,
  author =       "Jonathan M. Borwein",
  title =        "{Ramanujan}'s {AGM} Continued Fractions and Dynamics:
                 the real case",
  day =          "4",
  month =        mar,
  year =         "2004",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, Mathematics Department, Dalhousie
                 University, Halifax, NS, Canada.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:2004:RACb,
  author =       "Jonathan M. Borwein",
  title =        "{Ramanujan}'s {AGM} Continued Fractions and Dynamics:
                 the complex case",
  day =          "10",
  month =        mar,
  year =         "2004",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Analysis Seminar, Mathematics Department, Dalhousie
                 University, Halifax, NS, Canada.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:2004:RACc,
  author =       "Jonathan M. Borwein",
  title =        "{Ramanujan}'s {AGM} Continued Fractions and Dynamics",
  day =          "27",
  month =        aug,
  year =         "2004",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Workshop on Analytic and Computational Number Theory,
                 August 23--27, Dalhousie University, Halifax, NS,
                 Canada.",
  acknowledgement = ack-nhfb,
}

@Article{Borwein:2004:RAFa,
  author =       "J. Borwein and R. Crandall and G. Fee",
  title =        "On the {Ramanujan} {AGM} fraction. {I}. {The}
                 real-parameter case",
  journal =      j-EXP-MATH,
  volume =       "13",
  number =       "3",
  pages =        "275--285",
  month =        "????",
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2004.10504540",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11J70 (11A55 33C05 40A15)",
  MRnumber =     "2103326 (2005g:11126)",
  MRreviewer =   "James G. Mc Laughlin",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/27/;
                 http://projecteuclid.org/euclid.em/1103749836",
  acknowledgement = ack-nhfb,
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
}

@Article{Borwein:2004:RAFb,
  author =       "J. Borwein and R. Crandall",
  title =        "On the {Ramanujan} {AGM} fraction. {II}. {The}
                 complex-parameter case",
  journal =      j-EXP-MATH,
  volume =       "13",
  number =       "3",
  pages =        "287--295",
  month =        "????",
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2004.10504541",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11J70 (11A55 33C05)",
  MRnumber =     "2103327 (2005h:11149)",
  MRreviewer =   "James G. Mc Laughlin",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/29/;
                 http://projecteuclid.org/euclid.em/1103749837",
  acknowledgement = ack-nhfb,
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
}

@Article{Bullen:2004:GAM,
  author =       "P. S. Bullen",
  title =        "The geometric--arithmetic mean inequality",
  journal =      "J. Indones. Math. Soc.",
  volume =       "10",
  number =       "2",
  pages =        "99--102",
  year =         "2004",
  ISSN =         "0854-1388",
  MRclass =      "26D15",
  MRnumber =     "2097093",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Indonesian Mathematical Society.
                 Majalah Ilmiah Himpunan Matematika Indonesia (MIHMI)",
}

@InCollection{Cox:2004:AGM,
  author =       "David A. Cox",
  title =        "The Arithmetic--Geometric Mean of {Gauss}",
  crossref =     "Berggren:2004:PSB",
  pages =        "481--536",
  year =         "2004",
  DOI =          "https://doi.org/10.1007/978-1-4757-4217-6_55",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_55",
  acknowledgement = ack-nhfb,
}

@Article{Ovesea-Tudor:2004:UCC,
  author =       "Horiana Ovesea-Tudor",
  title =        "Univalence criteria connected with arithmetic and
                 geometric means",
  journal =      "Studia Univ. Babe{\c{s}}-Bolyai Math.",
  volume =       "49",
  number =       "1",
  pages =        "55--62",
  year =         "2004",
  ISSN =         "0252-1938",
  MRclass =      "30C55",
  MRnumber =     "2140514",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Universitatis Babe{\c{s}}-Bolyai. Studia.
                 Mathematica",
}

@InCollection{Salamin:2004:CUA,
  author =       "Eugene Salamin",
  title =        "Computation of $ \pi $ Using Arithmetic--Geometric
                 Mean",
  crossref =     "Berggren:2004:PSB",
  pages =        "418--423",
  year =         "2004",
  DOI =          "https://doi.org/10.1007/978-1-4757-4217-6_46",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_46",
  acknowledgement = ack-nhfb,
}

@Article{Mihesan:2005:RPT,
  author =       "Vasile Mihe{\c{s}}an",
  title =        "{Rado} and {Popoviciu} type inequalities for pseudo
                 arithmetic and geometric means",
  journal =      j-INT-J-PURE-APPL-MATH,
  volume =       "23",
  number =       "3",
  pages =        "293--297",
  year =         "2005",
  ISSN =         "1311-8080 (print), 1314-3395 (electronic)",
  ISSN-L =       "1314-3395",
  MRclass =      "26D15 (26E60)",
  MRnumber =     "2176202",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Pure and Applied
                 Mathematics",
  journal-URL =  "http://ijpam.eu/",
}

@Article{Wu:2005:SRE,
  author =       "Shanhe Wu",
  title =        "Some results on extending and sharpening the
                 {Weierstrass} product inequalities",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "308",
  number =       "2",
  pages =        "689--702",
  year =         "2005",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/j.jmaa.2004.11.064",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X04010157",
  abstract =     "In this paper, we establish two extensions of
                 Weierstrass's inequality involving symmetric functions
                 by means of the theory of majorization, and give an
                 interesting sharpness of Weierstrass's inequality by
                 using the arithmetic--geometric mean inequality.
                 Furthermore, we apply these results to improve a
                 well-known inequality and deduce some new
                 inequalities.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "Arithmetic--geometric mean inequality; Elementary
                 symmetric function; Majorization; Schur-concave
                 function; Weierstrass's inequality",
}

@Article{Bhatia:2006:IAG,
  author =       "Rajendra Bhatia",
  title =        "Interpolating the arithmetic--geometric mean
                 inequality and its operator version",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "413",
  number =       "2--3",
  pages =        "355--363",
  day =          "1",
  month =        mar,
  year =         "2006",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2005.03.005",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "47A63 (15A48)",
  MRnumber =     "2198940",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2000.bib",
  note =         "Special Issue on the 11th Conference of the
                 International Linear Algebra Society, Coimbra, 200411th
                 Conference of the International Linear Algebra Society,
                 Coimbra, 2004",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379505001382",
  abstract =     "Two families of means (called Heinz means and Heron
                 means) that interpolate between the geometric and the
                 arithmetic mean are considered. Comparison inequalities
                 between them are established. Operator versions of
                 these inequalities are obtained. Failure of such
                 extensions in some cases is illustrated by a simple
                 example.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Inequalities for means; Operator inequalities;
                 Positive definite matrix; Unitarily invariant norm",
}

@TechReport{Brent:2006:FAH,
  author =       "Richard P. Brent",
  title =        "Fast Algorithms for High-Precision Computation of
                 Elementary Functions",
  type =         "Report",
  number =       "??",
  institution =  "Australian National University",
  address =      "Canberra, ACT 0200, Australia",
  pages =        "61",
  day =          "12",
  month =        jul,
  year =         "2006",
  bibdate =      "Fri Sep 04 16:33:10 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://rnc7.loria.fr/brent_invited.pdf;
                 https://maths-people.anu.edu.au/~brent/pd/RNC7t.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic-geometric mean",
  remark =       "From page 57: ``This talk is based on a chapter of a
                 book that Paul Zimmermann and I are writing''. That
                 book is entry \cite{Brent:2011:MCA}.",
}

@Article{Enge:2006:CCP,
  author =       "Andreas Enge",
  title =        "The complexity of class polynomial computation via
                 floating point approximations",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "24",
  month =        jan,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in Mathematics of Computation 78, {\bf 266}
                 (2009) 1089--1107.",
  URL =          "http://arxiv.org/abs/cs/0601104",
  abstract =     "We analyse the complexity of computing class
                 polynomials, that are an important ingredient for CM
                 constructions of elliptic curves, via complex floating
                 point approximations of their roots. The heart of the
                 algorithm is the evaluation of modular functions in
                 several arguments. The fastest one of the presented
                 approaches uses a technique devised by Dupont to
                 evaluate modular functions by Newton iterations on an
                 expression involving the arithmetic--geometric mean. It
                 runs in time $ O (|D| \log^5 |D| \log \log |D|) = O
                 (|D|^{1 + \epsilon }) = O (h^{2 + \epsilon }) $ for any
                 $ \epsilon > 0 $, where $D$ is the CM discriminant and
                 $h$ is the degree of the class polynomial. Another fast
                 algorithm uses multipoint evaluation techniques known
                 from symbolic computation; its asymptotic complexity is
                 worse by a factor of $ \log |D|$. Up to logarithmic
                 factors, this running time matches the size of the
                 constructed polynomials. The estimate also relies on a
                 new result concerning the complexity of enumerating the
                 class group of an imaginary-quadratic order and on a
                 rigorously proven upper bound for the height of class
                 polynomials.",
  acknowledgement = ack-nhfb,
  subject =      "Numerical Analysis (cs.NA); Symbolic Computation
                 (cs.SC); Number Theory (math.NT)",
}

@Article{Holland:2006:IBC,
  author =       "Finbarr Holland",
  title =        "An inequality between compositions of weighted
                 arithmetic and geometric means",
  journal =      j-JIPAM-J-INEQUAL-PURE-APPL-MATH,
  volume =       "7",
  number =       "5",
  pages =        "Article 159, 8",
  year =         "2006",
  ISSN =         "1443-5756",
  MRclass =      "26D15 (26E60)",
  MRnumber =     "2268614",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "JIPAM. Journal of Inequalities in Pure and Applied
                 Mathematics",
  journal-URL =  "http://www.emis.de/journals/JIPAM/",
}

@Article{Liu:2006:OTA,
  author =       "Lei Liu and Jian Hua Zhang",
  title =        "An operator-trace arithmetic--geometric mean
                 inequality",
  journal =      "J. Baoji Univ. Arts Sci. Math. Colloq. Chin. Univ.",
  volume =       "3B",
  number =       "3B",
  pages =        "208--209",
  year =         "2006",
  ISSN =         "1007-1261",
  MRclass =      "47A63",
  MRnumber =     "2268274",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Baoji University of Arts and Sciences. Math
                 Colloquium of Chinese Universities. Baoji Wenli Xueyuan
                 Xuebao. Daxue Shuxue Jikan",
}

@Article{Sabnis:2006:AAG,
  author =       "S. V. Sabnis and G. Agnihothram",
  title =        "Application of arithmetic--geometric mean inequality
                 for construction of reliability test plan for parallel
                 systems in the presence of covariates",
  journal =      j-ECON-QUAL-CONTROL,
  volume =       "21",
  number =       "2",
  pages =        "219--230",
  year =         "2006",
  DOI =          "https://doi.org/10.1515/EQC.2006.219",
  ISSN =         "0940-5151 (print), 1869-6147 (electronic)",
  MRclass =      "62N05 (62N03)",
  MRnumber =     "2364112",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Economic Quality Control",
  journal-URL =  "http://degruyter.com/eqc",
}

@Article{Taneja:2006:GAG,
  author =       "Inder Jeet Taneja",
  title =        "Generalized arithmetic and geometric mean divergence
                 measure and their statistical aspects",
  journal =      "J. Interdiscip. Math.",
  volume =       "9",
  number =       "2",
  pages =        "249--266",
  year =         "2006",
  DOI =          "https://doi.org/10.1080/09720502.2006.10700442",
  ISSN =         "0972-0502",
  MRclass =      "62B10",
  MRnumber =     "2245159",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Interdisciplinary Mathematics",
}

@Article{Tao:2006:MRS,
  author =       "Yunxing Tao",
  title =        "More results on singular value inequalities of
                 matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "416",
  number =       "2--3",
  pages =        "724--729",
  year =         "2006",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2005.12.017",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379506000024",
  abstract =     "The arithmetic--geometric mean inequality for singular
                 values due to Bhatia and Kittaneh says that $ 2 s_j (A
                 B^\star) \leq s_j (A^\star A + B^\star B) $, $ j = 1,
                 2, \ldots $ for any matrices $A$, $B$. We give a new
                 equivalent form and some relevant generalizations of
                 this inequality. In particular, we show that $ s_j
                 (A^{1 / 4} B^{3 / 4} + A^{3 / 4} B^{1 / 4}) \leq s_j (A
                 + B)$, $ j = 1, \ldots, n$ for any $ n \times n $
                 positive semidefinite matrices $A$, $B$, which proves a
                 special case of Zhan's conjecture posed in 2000.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Arithmetic--geometric mean; Positive semidefinite
                 matrix; Singular value",
}

@Article{Yamazaki:2006:EKI,
  author =       "Takeaki Yamazaki",
  title =        "An extension of {Kantorovich} inequality to
                 $n$-operators via the geometric mean by
                 {Ando--Li--Mathias}",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "416",
  number =       "2--3",
  pages =        "688--695",
  year =         "2006",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2005.12.013",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S002437950500604X",
  abstract =     "In this paper, we shall extend Kantorovich inequality.
                 This is an estimate by using the geometric mean of
                 n-operators which have been defined by
                 Ando--Li--Mathias in [T. Ando, C. K. Li, R. Mathias,
                 Geometric means, Linear Algebra Appl. 385 (2004)
                 305--334]. As a related result, we obtain a converse of
                 arithmetic--geometric means inequality of n-operators
                 via Kantorovich constant.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Arithmetic--geometric means inequality; Geometric mean
                 of n-operators; Kantorovich inequality; Specht's
                 ratio",
}

@Article{Aujla:2007:EIC,
  author =       "Jaspal Singh Aujla and Jean-Christophe Bourin",
  title =        "Eigenvalue inequalities for convex and log-convex
                 functions",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "424",
  number =       "1",
  pages =        "25--35",
  year =         "2007",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2006.02.027",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Special Issue in honor of Roger Horn",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379506001261",
  abstract =     "We give a matrix version of the scalar inequality $
                 f(a + b) \leq f(a) + f(b) $ for positive concave
                 functions $f$ on $ [0, \infty)$. We show that Choi's
                 inequality for positive unital maps and operator convex
                 functions remains valid for monotone convex functions
                 at the cost of unitary congruences. Some inequalities
                 for log-convex functions are presented and a new
                 arithmetic--geometric mean inequality for positive
                 matrices is given. We also point out a simple proof of
                 the Bhatia--Kittaneh arithmetic--geometric mean
                 inequality.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Convex function; Eigenvalue; Majorization; Unital
                 positive linear map",
}

@Article{Barnard:2007:IHA,
  author =       "Roger W. Barnard and Kendall C. Richards",
  title =        "On inequalities for hypergeometric analogues of the
                 arithmetic--geometric mean",
  journal =      j-JIPAM-J-INEQUAL-PURE-APPL-MATH,
  volume =       "8",
  number =       "3",
  pages =        "Article 65, 5",
  year =         "2007",
  ISSN =         "1443-5756",
  MRclass =      "26D15 (26E60 33C05)",
  MRnumber =     "2345920",
  MRreviewer =   "Giampietro Allasia",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "JIPAM. Journal of Inequalities in Pure and Applied
                 Mathematics",
  journal-URL =  "http://www.emis.de/journals/JIPAM/",
}

@Article{Hirschhorn:2007:GI,
  author =       "M. D. Hirschhorn",
  title =        "The {AM--GM} inequality",
  journal =      j-MATH-INTEL,
  volume =       "29",
  number =       "4",
  pages =        "7--??",
  month =        "????",
  year =         "2007",
  CODEN =        "MAINDC",
  DOI =          "https://doi.org/10.1007/BF02986168",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  bibdate =      "Fri Feb 15 16:15:39 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  ZMnumber =     "1225.00022",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Intelligencer",
  journal-URL =  "http://link.springer.com/journal/283",
  ZMclass =      "00A35 (Methodology of mathematics, didactics); 26D15
                 (Inequalities for sums, series and integrals of real
                 functions); 97I20 (Mappings and functions (educational
                 aspects))",
}

@Article{Kim:2007:CIH,
  author =       "Sejong Kim and Yongdo Lim",
  title =        "A converse inequality of higher order weighted
                 arithmetic and geometric means of positive definite
                 operators",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "426",
  number =       "2--3",
  pages =        "490--496",
  day =          "15",
  month =        oct,
  year =         "2007",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2007.05.028",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "47A63",
  MRnumber =     "2350672",
  MRreviewer =   "Chia-Shiang Lin",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379507002455",
  abstract =     "In this paper we consider weighted arithmetic and
                 geometric means of higher orders constructed by the
                 symmetrization method appeared in Ando--Li--Mathias's
                 definition of multi-variable geometric means and the
                 arithmetic--geometric mean inequality of higher order
                 weighted version. We establish a converse inequality of
                 higher order weighed arithmetic and geometric means via
                 Specht ratio.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Arithmetic--geometric mean inequality; Higher order
                 weighted geometric mean; Positive definite operator;
                 Specht ratio",
}

@Book{King:2007:DNC,
  author =       "Louis Vessot King",
  title =        "On the Direct Numerical Calculation of Elliptic
                 Functions and Integrals",
  publisher =    "Mellon Press",
  address =      "",
  pages =        "56",
  year =         "2007",
  ISBN =         "1-4067-4226-0",
  ISBN-13 =      "978-1-4067-4226-8",
  LCCN =         "",
  bibdate =      "Wed Feb 03 08:53:04 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  remark =       "The AGM method for Jacobian elliptic was discovered by
                 this book's author at McGill University in 1913, first
                 published in \cite{King:1921:SNF}, and then in a 1924
                 monograph, of which this is a reprint.",
}

@Article{Koike:2007:IFP,
  author =       "Kenji Koike and Hironori Shiga",
  title =        "Isogeny formulas for the {Picard} modular form and a
                 three terms arithmetic geometric mean",
  journal =      j-J-NUMBER-THEORY,
  volume =       "124",
  number =       "1",
  pages =        "123--141",
  month =        may,
  year =         "2007",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2006.08.002",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  MRclass =      "11F55",
  MRnumber =     "2320994",
  MRreviewer =   "Enrique Gonz{\'a}lez-Jim{\'e}nez",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X06002058",
  abstract =     "In this paper we study the Picard modular forms and
                 show a new three terms arithmetic geometric mean (AGM)
                 system. This AGM system is expressed via the Appell
                 hypergeometric function of two variables. The Picard
                 modular forms are expressed via the theta constants,
                 and they give the modular function for the family of
                 Picard curves. Our theta constants are ``Neben type''
                 modular forms of weight 1 defined on the complex
                 2-dimensional hyperball with respect to an index finite
                 subgroup of the Picard modular group. We define a
                 simultaneous 3-isogeny for the family of Jacobian
                 varieties of Picard curves. Our main theorem shows the
                 explicit relations between two systems of theta
                 constants which are corresponding to isogenous Jacobian
                 varieties. This relation induces a new three terms AGM
                 which is a generalization of Borweins' cubic AGM.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Lehavi:2007:EFA,
  author =       "D. Lehavi and C. Ritzenthaler",
  title =        "An Explicit Formula for the Arithmetic--Geometric Mean
                 in Genus $3$",
  journal =      j-EXP-MATH,
  volume =       "16",
  number =       "4",
  pages =        "421--440",
  month =        "????",
  year =         "2007",
  CODEN =        "????",
  ISSN =         "1058-6458 (print), 1944-950x (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "14H40 (14H45 14Q05)",
  MRnumber =     "2378484",
  MRreviewer =   "Mich{\`e}le Pelletier",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib;
                 http://www.tandfonline.com/toc/uexm20/16/4",
  URL =          "http://projecteuclid.org/euclid.em/1204836513",
  acknowledgement = ack-nhfb,
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
}

@Article{Tanimoto:2007:NOA,
  author =       "Shinji Tanimoto",
  title =        "A novel operation associated with {Gauss}'
                 arithmetic--geometric means",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--6",
  day =          "27",
  month =        aug,
  year =         "2007",
  bibdate =      "Tue Mar 14 18:08:54 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "https://arxiv.org/pdf/0708.3521.pdf",
  abstract =     "The arithmetic mean is the mean for addition and the
                 geometric mean is that for multiplication. Then what
                 kind of binary operation is associated with the
                 arithmetic--geometric mean (AGM) due to C. F. Gauss? If
                 it is possible to construct an arithmetic operation
                 such that AGM is the mean for this operation, it can be
                 regarded as an intermediate operation between addition
                 and multiplication in view of the meaning of AGM. In
                 this paper such an operation is introduced and several
                 of its algebraic properties are proved.",
  acknowledgement = ack-nhfb,
}

@Article{Walden:2007:HMI,
  author =       "Byron L. Walden and Lesley A. Ward",
  title =        "A harmonic measure interpretation of the
                 arithmetic--geometric mean",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "114",
  number =       "7",
  pages =        "610--622",
  year =         "2007",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "31A15 (26E60 28A12 30C20 30C85 33C45)",
  MRnumber =     "2341324",
  MRreviewer =   "Dimitrios Betsakos",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Aldaz:2008:RIB,
  author =       "J. M. Aldaz",
  title =        "A refinement of the inequality between arithmetic and
                 geometric means",
  journal =      j-J-MATH-INEQUAL,
  volume =       "2",
  number =       "4",
  pages =        "473--477",
  year =         "2008",
  DOI =          "https://doi.org/10.7153/jmi-02-42",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "26D15 (26E60)",
  MRnumber =     "2482460",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Bhatia:2008:MAG,
  author =       "Rajendra Bhatia and Fuad Kittaneh",
  title =        "The matrix arithmetic--geometric mean inequality
                 revisited",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "428",
  number =       "8--9",
  pages =        "2177--2191",
  day =          "15",
  month =        apr,
  year =         "2008",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2007.11.030",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A42 (47A30 47A63)",
  MRnumber =     "2401646",
  MRreviewer =   "Omar Hirzallah",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379507005381",
  abstract =     "Ideas related to matrix versions of the
                 arithmetic--geometric mean inequality are explained.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Matrix inequalities; Matrix monotone functions;
                 Pinching; Singular values; Unitarily invariant norms",
}

@Article{Carvalhaes:2008:APS,
  author =       "Claudio G. Carvalhaes and Patrick Suppes",
  title =        "Approximations for the period of the simple pendulum
                 based on the arithmetic--geometric mean",
  journal =      j-AMER-J-PHYSICS,
  volume =       "76",
  number =       "12",
  pages =        "1150--1154",
  month =        dec,
  year =         "2008",
  CODEN =        "AJPIAS",
  DOI =          "https://doi.org/10.1119/1.2968864",
  ISSN =         "0002-9505 (print), 1943-2909 (electronic)",
  ISSN-L =       "0002-9505",
  bibdate =      "Tue Mar 14 18:22:35 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "See comments in \cite{Villarino:2014:ASP} about prior
                 work before 1966 by Albert Edward Ingham (1900--1967)
                 producing both upper and lower bounds to approximations
                 to the period of a pendulum.",
  URL =          "http://aapt.scitation.org/doi/full/10.1119/1.2968864",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Physics",
  journal-URL =  "http://scitation.aip.org/content/aapt/journal/ajp",
  remark =       "From the introduction: ``The lack of an elementary
                 closed-form restricts the study of the simple pendulum
                 at the undergraduate level to small oscillations.
                 \ldots{} convergence with eight digits of accuracy is
                 obtained for an amplitude of $ 179^\circ $ after only
                 four iterations.''",
}

@Article{Feng:2008:MVS,
  author =       "Bao Qi Feng and Andrew Tonge",
  title =        "Matrix versions of some refinements of the
                 arithmetic--geometric mean inequality",
  journal =      j-J-MATH-SCI-ADV-APPL,
  volume =       "1",
  number =       "2",
  pages =        "243--264",
  year =         "2008",
  ISSN =         "0974-5750",
  MRclass =      "26E60 (15A45)",
  MRnumber =     "2530506",
  MRreviewer =   "Alan L. Horwitz",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Sciences. Advances and
                 Applications",
  journal-URL =  "http://www.scientificadvances.co.in/about-this-journal/1",
}

@Article{Ito:2008:MAG,
  author =       "Takashi Ito",
  title =        "Mixed arithmetic and geometric means and related
                 inequalities",
  journal =      j-JIPAM-J-INEQUAL-PURE-APPL-MATH,
  volume =       "9",
  number =       "3",
  pages =        "Article 65, 21",
  year =         "2008",
  ISSN =         "1443-5756",
  MRclass =      "26D20 (26E60)",
  MRnumber =     "2476645",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "JIPAM. Journal of Inequalities in Pure and Applied
                 Mathematics",
  journal-URL =  "http://www.emis.de/journals/JIPAM/",
}

@Article{Jarvis:2008:HGA,
  author =       "Frazer Jarvis",
  title =        "Higher genus arithmetic--geometric means",
  journal =      j-RAMANUJAN-J,
  volume =       "17",
  number =       "1",
  pages =        "1--17",
  year =         "2008",
  CODEN =        "RAJOF9",
  DOI =          "https://doi.org/10.1007/s11139-007-9058-0",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  MRclass =      "14K25 (11B83 11F27)",
  MRnumber =     "2439522",
  MRreviewer =   "Cristiana Bertolin",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Ramanujan Journal. An International Journal Devoted to
                 the Areas of Mathematics Influenced by Ramanujan",
  journal-URL =  "http://link.springer.com/journal/11139",
}

@Article{Koike:2008:EGA,
  author =       "Kenji Koike and Hironori Shiga",
  title =        "An extended {Gauss} {AGM} and corresponding {Picard}
                 modular forms",
  journal =      j-J-NUMBER-THEORY,
  volume =       "128",
  number =       "7",
  pages =        "2097--2126",
  month =        jul,
  year =         "2008",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2007.12.001",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Tue Mar 14 17:07:32 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X08000218",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Lorentzen:2008:CDR,
  author =       "Lisa Lorentzen",
  title =        "Convergence and divergence of the {Ramanujan} {AGM}
                 fraction",
  journal =      j-RAMANUJAN-J,
  volume =       "16",
  number =       "1",
  pages =        "83--95",
  month =        may,
  year =         "2008",
  DOI =          "https://doi.org/10.1007/s11139-007-9112-y",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  bibdate =      "Tue Mar 14 15:27:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  abstract =     "We prove that the Ramanujan AGM fraction diverges if $
                 |a| = |b| $ with $ a^2 \neq b^2 $. Thereby we prove two
                 conjectures posed by J. Borwein and R. Crandall. We
                 also demonstrate a method for accelerating the
                 convergence of this continued fraction when it
                 converges.",
  acknowledgement = ack-nhfb,
  fjournal =     "The {Ramanujan} Journal",
  journal-URL =  "http://link.springer.com/journal/11139",
}

@Article{Micic:2008:IIA,
  author =       "Jadranka Mi{\'c}i{\'c} and Josip Pe{\v{c}}ari{\'c} and
                 Vidosava {\v{S}}imi{\'c}",
  title =        "Inequalities involving the arithmetic and geometric
                 operator means",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "11",
  number =       "3",
  pages =        "415--430",
  year =         "2008",
  DOI =          "https://doi.org/10.7153/mia-11-31",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "47A63",
  MRnumber =     "2431206",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Uchida:2008:SPG,
  author =       "Yasuharu Uchida",
  title =        "A simple proof of the geometric--arithmetic mean
                 inequality",
  journal =      j-JIPAM-J-INEQUAL-PURE-APPL-MATH,
  volume =       "9",
  number =       "2",
  pages =        "Article 56, 2",
  year =         "2008",
  ISSN =         "1443-5756",
  MRclass =      "26E60",
  MRnumber =     "2417338",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "JIPAM. Journal of Inequalities in Pure and Applied
                 Mathematics",
  journal-URL =  "http://www.emis.de/journals/JIPAM/",
}

@Article{Yeh:2008:SEF,
  author =       "Cheh-Chih Yeh and Hung-Wen Yeh and Wenyaw Chan",
  title =        "Some equivalent forms of the arithmetic--geometric
                 mean inequality in probability: a survey",
  journal =      j-J-INEQUAL-APPL,
  pages =        "Art. ID 386715, 9",
  year =         "2008",
  ISSN =         "1025-5834",
  ISSN-L =       "1025-5834",
  MRclass =      "26E60 (60E15)",
  MRnumber =     "2449062",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Inequalities and Applications",
  journal-URL =  "http://journalofinequalitiesandapplications.springeropen.com/",
}

@Article{Aldaz:2009:SII,
  author =       "J. M. Aldaz",
  title =        "Self-improvement of the inequality between arithmetic
                 and geometric means",
  journal =      j-J-MATH-INEQUAL,
  volume =       "3",
  number =       "2",
  pages =        "213--216",
  year =         "2009",
  DOI =          "https://doi.org/10.7153/jmi-03-21",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "26D15",
  MRnumber =     "2542299",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Cheon:2009:RBS,
  author =       "Gi-Sang Cheon and Andrew W. Eckford",
  title =        "A relationship between subpermanents and the
                 arithmetic--geometric mean inequality",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "430",
  number =       "1",
  pages =        "114--120",
  day =          "1",
  month =        jan,
  year =         "2009",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2008.07.001",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A15 (15A48)",
  MRnumber =     "2460503",
  MRreviewer =   "Carlos M. da Fonseca",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379508003406",
  abstract =     "Using the arithmetic--geometric mean inequality, we
                 give bounds for k-subpermanents of nonnegative $ n
                 \times n $ matrices $F$. In the case $ k = n$, we
                 exhibit an $ n^2$-set $S$ whose arithmetic and
                 geometric means constitute upper and lower bounds for $
                 \per (F) / n!$. We offer sharpened versions of these
                 bounds when $F$ has zero-valued entries.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "AM--GM inequality; Permanent; Subpermanent",
}

@Article{Furuichi:2009:TIP,
  author =       "Shigeru Furuichi and Ken Kuriyama and Kenjiro Yanagi",
  title =        "Trace inequalities for products of matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "430",
  number =       "8--9",
  pages =        "2271--2276",
  year =         "2009",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2008.12.003",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379508005685",
  abstract =     "In this short paper, we study some trace inequalities
                 of the products of the matrices and the power of
                 matrices by the use of elementary calculations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Arithmetic--geometric mean inequality and nonnegative
                 matrix; Matrix trace inequalitiy",
}

@Article{Hayashi:2009:NCA,
  author =       "Tomohiro Hayashi",
  title =        "Non-commutative arithmetic--geometric mean
                 inequality",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "137",
  number =       "10",
  pages =        "3399--3406",
  year =         "2009",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/S0002-9939-09-09911-0",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "47A63",
  MRnumber =     "2515409",
  MRreviewer =   "{\`E}dward L. Pekarev",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@Article{Kim:2009:SCI,
  author =       "Sejong Kim and Hosoo Lee and Yongdo Lim",
  title =        "A sharp converse inequality of three weighted
                 arithmetic and geometric means of positive definite
                 operators",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "12",
  number =       "3",
  pages =        "519--523",
  year =         "2009",
  DOI =          "https://doi.org/10.7153/mia-12-40",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "47A63",
  MRnumber =     "2540975",
  MRreviewer =   "Pedro Tradacete",
  bibdate =      "Tue Aug 15 10:24:29 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Kosheleva:2009:GNJ,
  author =       "O. Kosheleva and V. Kreinovich",
  title =        "Guesstimation: a New Justification of the Geometric
                 Mean Heuristic",
  journal =      j-APPL-MATH-SCI-RUSE,
  volume =       "3",
  number =       "47",
  pages =        "2335--2342",
  year =         "2009",
  ISSN =         "1312-885x (print), 1314-7552 (electronic)",
  MRclass =      "62F10",
  MRnumber =     "MR2558236 (2010i:62055)",
  bibdate =      "Fri Oct 15 09:08:58 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.cs.utep.edu/vladik/2009/tr09-10.pdf;
                 http://www.openj-gate.com/Browse/ArticleList.aspx?Journal_id=124136&issue_id=1153557",
  abstract =     "In many practical situations in which the only
                 information we have about the quantity $x$ is that its
                 value is within an interval $ [\underbar {x}; \overbar
                 {x}]$, a responsible estimate for this quantity is the
                 geometric mean of the bounds $ \sqrt {\underbar {x}
                 \cdot \overbar {x}}$. In this paper, we provide a new
                 justification for this geometric mean heuristic.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematical Sciences (Ruse)",
  journal-URL =  "http://www.m-hikari.com/ams/",
  keywords =     "arithmetic mean; geometric mean; interval arithmetic",
}

@Article{Lekner:2009:ASC,
  author =       "John Lekner",
  title =        "Axially symmetric charge distributions and the
                 arithmetic--geometric mean",
  journal =      j-J-ELECTROST,
  volume =       "67",
  number =       "6",
  pages =        "880--885",
  year =         "2009",
  CODEN =        "JOELDH",
  DOI =          "https://doi.org/10.1016/j.elstat.2009.07.007",
  ISSN =         "0304-3886 (print), 1873-5738 (electronic)",
  ISSN-L =       "0304-3886",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0304388609001806",
  abstract =     "The potential at an arbitrary point in space due to an
                 axially symmetric charge distribution is related to the
                 arithmetic--geometric mean of the maximum and minimum
                 distances from each annulus of constant charge density.
                 The arithmetic--geometric mean is expressible in terms
                 of the elliptic integral of the first kind, $K$. Thus
                 the potential of a charged body with cylindrical
                 symmetry is reducible to a double integral over the
                 charge density times $K$. For conductors the charge
                 resides on the surface, and the potential reduces to a
                 single integral over the surface charge density times
                 $K$. This result leads to a new proof of the relation
                 between a sum over products of Legendre polynomials and
                 the complete elliptic integral of the first kind, and
                 to new identities for the angular average of Legendre
                 polynomials divided by $ | r - r' |$. The method also
                 provides a direct route to the capacitance of a slender
                 torus, without the use of toroidal coordinates.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Electrost.",
  fjournal =     "Journal of Electrostatics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043886",
  keywords =     "Arithmetic--geometric mean; Axially symmetric charge
                 distributions; Thin torus",
}

@Article{Qi:2009:AUP,
  author =       "Feng Qi and Anthony Sofo",
  title =        "An alternative and united proof of a double inequality
                 for bounding the arithmetic--geometric mean",
  journal =      "Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl.
                 Math. Phys.",
  volume =       "71",
  number =       "3",
  pages =        "69--76",
  year =         "2009",
  ISSN =         "1223-7027",
  MRclass =      "26E60 (26D15)",
  MRnumber =     "2553929",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "``Politehnica'' University of Bucharest. Scientific
                 Bulletin. Series A. Applied Mathematics and Physics",
}

@Article{Raissouli:2009:AGH,
  author =       "Mustapha Ra{\"\i}ssouli and Fatima Leazizi and Mohamed
                 Chergui",
  title =        "Arithmetic--geometric--harmonic mean of three positive
                 operators",
  journal =      j-JIPAM-J-INEQUAL-PURE-APPL-MATH,
  volume =       "10",
  number =       "4",
  pages =        "Article 117, 11",
  year =         "2009",
  ISSN =         "1443-5756",
  MRclass =      "15B48 (47A64)",
  MRnumber =     "2577887",
  MRreviewer =   "Mohammad Sal Moslehian",
  bibdate =      "Tue Aug 15 10:18:13 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "JIPAM. Journal of Inequalities in Pure and Applied
                 Mathematics",
  journal-URL =  "http://www.emis.de/journals/JIPAM/",
}

@Article{Aldaz:2010:CRB,
  author =       "J. M. Aldaz",
  title =        "Concentration of the ratio between the geometric and
                 arithmetic means",
  journal =      j-J-THEOR-PROBAB,
  volume =       "23",
  number =       "2",
  pages =        "498--508",
  year =         "2010",
  CODEN =        "JTPREO",
  DOI =          "https://doi.org/10.1007/s10959-009-0215-9",
  ISSN =         "0894-9840 (print), 1572-9230 (electronic)",
  ISSN-L =       "0894-9840",
  MRclass =      "26E60 (26D15 28A75 60D05)",
  MRnumber =     "2644872",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Theoretical Probability",
  journal-URL =  "http://link.springer.com/journal/10959",
}

@InCollection{Arndt:2010:AEI,
  author =       "J{\"o}rg Arndt",
  title =        "The {AGM}, elliptic integrals, and algorithms for
                 computing $ \pi $",
  crossref =     "Arndt:2011:MC",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "599--621",
  year =         "2011",
  DOI =          "https://doi.org/10.1007/978-3-642-14764-7_31",
  bibdate =      "Tue Mar 14 15:06:12 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Unpublished{Brent:2010:MPZ,
  author =       "Richard P. Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  day =          "20",
  month =        apr,
  year =         "2010",
  MRclass =      "11Y60 (Primary), 65Y20 (Secondary)",
  bibdate =      "Tue Apr 26 14:13:36 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  note =         "Reprint of \cite{Brent:1976:MPZ} with a postscript
                 describing more recent developments. See also
                 \cite{Salamin:1976:CUA}",
  URL =          "http://arxiv.org/abs/1004.3412v2;
                 http://wwwmaths.anu.edu.au/~brent/pub/pub028.html",
  abstract =     "We consider methods for finding high-precision
                 approximations to simple zeros of smooth functions. As
                 an application, we give fast methods for evaluating the
                 elementary functions $ \log (x) $, $ \exp (x) $, $ \sin
                 (x) $ etc. to high precision. For example, if $x$ is a
                 positive floating-point number with an $n$-bit
                 fraction, then (under rather weak assumptions) an
                 $n$-bit approximation to $ \log (x)$ or $ \exp (x)$ may
                 be computed in time asymptotically equal to $ 13 M(n)
                 \lg (n)$, where $ M(n)$ is the time required to
                 multiply floating-point numbers with $n$-bit fractions.
                 Similar results are given for the other elementary
                 functions. Some analogies with operations on formal
                 power series (over a field of characteristic zero) are
                 discussed. In particular, it is possible to compute the
                 first $n$ terms in $ \log (1 + a_1 x + \cdots)$ or $
                 \exp (a_1. x) + \cdots $ in time $ O(M(n))$, where $
                 M(n)$ is the time required to multiply two polynomials
                 of degree $ n - 1$. It follows that the first $n$ terms
                 in a $q$-th power $ (1 + a_1 x + \cdots)^q$ can be
                 computed in time $ O(M(n))$, independent of $q$. One of
                 the results of this paper is the ``Gauss--Legendre'' or
                 ``Brent--Salamin'' algorithm for computing pi. This is
                 the first quadratically convergent algorithm for pi. It
                 was also published in Brent [J. ACM 23 (1976),
                 242--251], and independently by Salamin [Math. Comp. 30
                 (1976), 565--570].",
  acknowledgement = ack-nhfb,
}

@Article{Brent:2010:UAE,
  author =       "Richard P. Brent",
  title =        "Unrestricted algorithms for elementary and special
                 functions",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--13",
  month =        apr,
  year =         "2010",
  bibdate =      "Sat Feb 25 10:56:45 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/1004.3621",
  abstract =     "We describe some ``unrestricted'' algorithms which are
                 useful for the computation of elementary and special
                 functions when the precision required is not known in
                 advance. Several general classes of algorithms are
                 identified and illustrated by examples. The topics
                 include: power series methods, use of halving
                 identities, asymptotic expansions, continued fractions,
                 recurrence relations, Newton's method, numerical
                 contour integration, and the arithmetic--geometric
                 mean. Most of the algorithms discussed are implemented
                 in the MP package.",
  acknowledgement = ack-nhfb,
}

@Article{Cardenas-Barron:2010:EMD,
  author =       "Leopoldo Eduardo C{\'a}rdenas-Barr{\'o}n",
  title =        "An easy method to derive {EOQ} and {EPQ} inventory
                 models with backorders",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "59",
  number =       "2",
  pages =        "948--952",
  year =         "2010",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/j.camwa.2009.09.013",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122109006774",
  abstract =     "Recently, a cost minimization method to determine the
                 lot size for the EOQ/EPQ models with backorders was
                 published. This method is based on the well-known
                 arithmetic--geometric mean inequality. Although the
                 cost minimization method is correct and interesting, it
                 does not focus on deriving the backorders level. This
                 paper proposes another simple approach. The proposed
                 method finds both the lot size and the backorders
                 level.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Algebraic optimization; Arithmetic--geometric mean
                 (AGM) inequality; Backorders level;
                 Cauchy--Bunyakovsky--Schwarz (CBS) inequality; Cost
                 comparisons optimization; Economic order quantity;
                 Economic production quantity",
}

@Article{Cardenas-Barron:2010:SMC,
  author =       "Leopoldo Eduardo C{\'a}rdenas-Barr{\'o}n",
  title =        "A simple method to compute economic order quantities:
                 Some observations",
  journal =      j-APPL-MATH-MODEL,
  volume =       "34",
  number =       "6",
  pages =        "1684--1688",
  year =         "2010",
  CODEN =        "AMMODL",
  DOI =          "https://doi.org/10.1016/j.apm.2009.08.024",
  ISSN =         "0307-904x (print), 1872-8480 (electronic)",
  ISSN-L =       "0307-904X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0307904X09002777",
  abstract =     "Teng [2] presents an arithmetic--geometric mean method
                 to be applied to determine the optimal lot size for the
                 EOQ/EPQ models, taking into account backorders.
                 Although the arithmetic--geometric mean method is
                 correct, arguments as to when (not) to use the
                 arithmetic--geometric mean inequality as optimization
                 method are not complete. Moreover, this optimization
                 method does not focus on the method for deriving the
                 optimal backorders level. The main purpose of this work
                 is to overcome these shortcomings, presents a
                 discussion of when (not) to use the cost minimization
                 method and derives the optimal backorders level.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied mathematical modelling",
  keywords =     "Algebraic optimization; Arithmetic--geometric mean
                 optimization; Backorders; Cost comparisons
                 optimization; Cost-difference comparisons optimization;
                 EOQ/EPQ",
}

@Article{Kinjo:2010:AAG,
  author =       "Kensaku Kinjo and Yuken Miyasaka",
  title =        "$2$-{Adic} arithmetic--geometric mean and elliptic
                 curves",
  journal =      j-INTERDISCIP-INFORM-SCI,
  volume =       "16",
  number =       "1",
  pages =        "5--15",
  year =         "2010",
  DOI =          "https://doi.org/10.4036/iis.2010.5",
  ISSN =         "1340-9050 (print), 1347-6157 (electronic)",
  ISSN-L =       "1340-9050",
  MRclass =      "11S85 (11G07)",
  MRnumber =     "2648110",
  MRreviewer =   "Maria Sabitova",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Interdisciplinary Information Sciences",
  journal-URL =  "https://www.jstage.jst.go.jp/browse/iis",
}

@Article{Long:2010:OIG,
  author =       "Bo-Yong Long and Yu-Ming Chu",
  title =        "Optimal inequalities for generalized logarithmic,
                 arithmetic, and geometric means",
  journal =      j-J-INEQUAL-APPL,
  pages =        "806825:1--806825:10",
  year =         "2010",
  DOI =          "https://doi.org/10.1155/2010/806825",
  ISSN =         "1025-5834",
  ISSN-L =       "1025-5834",
  MRclass =      "26E60 (26D15)",
  MRnumber =     "2600201",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Inequalities and Applications",
  journal-URL =  "http://journalofinequalitiesandapplications.springeropen.com/",
}

@Article{Maksa:2010:ETF,
  author =       "Gyula Maksa and Adrienn Varga",
  title =        "The equivalence of two functional equations involving
                 the arithmetic mean, the geometric mean and their
                 {Gauss} composition",
  journal =      j-AEQUATIONES-MATHEMATICAE,
  volume =       "80",
  number =       "1-2",
  pages =        "173--179",
  year =         "2010",
  CODEN =        "AEMABN",
  DOI =          "https://doi.org/10.1007/s00010-010-0030-5",
  ISSN =         "0001-9054 (print), 1420-8903 (electronic)",
  ISSN-L =       "0001-9054",
  MRclass =      "39B22 (26E60)",
  MRnumber =     "2736948",
  MRreviewer =   "Tomasz Szostok",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Aequationes Mathematicae",
  journal-URL =  "http://link.springer.com/journal/10",
}

@Article{Matejicka:2010:POO,
  author =       "Ladislav Matej{\'\i}{\v{c}}ka",
  title =        "Proof of one optimal inequality for generalized
                 logarithmic, arithmetic, and geometric means",
  journal =      j-J-INEQUAL-APPL,
  pages =        "902432:1--902432:5",
  year =         "2010",
  DOI =          "https://doi.org/10.1155/2010/902432",
  ISSN =         "1025-5834",
  ISSN-L =       "1025-5834",
  MRclass =      "26E60 (26D20)",
  MRnumber =     "2738681",
  MRreviewer =   "Yu-ming Chu",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Inequalities and Applications",
  journal-URL =  "http://journalofinequalitiesandapplications.springeropen.com/",
}

@Article{Matsumoto:2010:AGM,
  author =       "Keiji Matsumoto and Tomohide Terasoma",
  title =        "Arithmetic--geometric means for hyperelliptic curves
                 and {Calabi--Yau} varieties",
  journal =      j-INT-J-MATH,
  volume =       "21",
  number =       "7",
  pages =        "939--949",
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S0129167X1000632X",
  ISSN =         "0129-167X",
  MRclass =      "14K20 (14J32 14K25)",
  MRnumber =     "2671531",
  MRreviewer =   "Ahmed Lesfari",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijm",
}

@Article{Solak:2010:NEN,
  author =       "S{\"u}leyman Solak and Mine Aytekin",
  title =        "A note on the {Euclidean} norms of matrices with
                 arithmetic--geometric harmonic means",
  journal =      j-APPL-MATH-SCI-RUSE,
  volume =       "4",
  number =       "29-32",
  pages =        "1553--1561",
  year =         "2010",
  ISSN =         "1312-885x (print), 1314-7552 (electronic)",
  MRclass =      "15A60",
  MRnumber =     "2643782",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematical Sciences",
  journal-URL =  "http://www.m-hikari.com/ams/",
}

@Article{Yamamoto:2010:HGA,
  author =       "Kouji Yamamoto and Nobuko Miyamoto and Sadao
                 Tomizawa",
  title =        "Harmonic, geometric and arithmetic means type
                 uncertainty measures for two-way contingency tables
                 with nominal categories",
  journal =      j-ADV-APPL-STAT,
  volume =       "17",
  number =       "2",
  pages =        "143--159",
  month =        aug,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "0972-3617",
  ISSN-L =       "0972-3617",
  MRclass =      "62H17",
  MRnumber =     "2789363",
  bibdate =      "Wed Aug 16 09:05:25 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advapplstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.pphmj.com/abstract/5234.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances and Applications in Statistics",
  journal-URL =  "http://www.pphmj.com/journals/contents/adas.htm",
}

@Article{Aldaz:2011:CDB,
  author =       "J. M. Aldaz",
  title =        "Comparison of differences between arithmetic and
                 geometric means",
  journal =      j-TAMKANG-J-MATH,
  volume =       "42",
  number =       "4",
  pages =        "453--462",
  year =         "2011",
  DOI =          "https://doi.org/10.5556/j.tkjm.42.2011.453-462",
  ISSN =         "0049-2930 (print), 2073-9826 (electronic)",
  ISSN-L =       "2073-9826",
  MRclass =      "26E60 (26D15)",
  MRnumber =     "2862349",
  MRreviewer =   "Alfred Witkowski",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tamkang Journal of Mathematics",
  journal-URL =  "http://journals.math.tku.edu.tw/index.php/TKJM",
}

@Article{Bayat:2011:AGM,
  author =       "M. Bayat and H. Teimoori",
  title =        "{Arithmetic--Geometric Mean} determinantal identity",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "435",
  number =       "11",
  pages =        "2936--2941",
  day =          "1",
  month =        dec,
  year =         "2011",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2011.05.031",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A24 (15A15)",
  MRnumber =     "2825293",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S002437951100440X",
  abstract =     "In this paper, we give a generalization of a
                 determinantal identity posed by Charles R. Johnson
                 about minors of a Toeplitz matrix satisfying a specific
                 matrix identity. These minors are those appear in the
                 Dodgson's condensation formula.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
  keywords =     "AGM (arithmetic--geometric mean);
                 Arithmetic--Geometric Mean; Determinantal identity;
                 Dodgson's condensation; Toeplitz matrix",
}

@Article{Bini:2011:NCM,
  author =       "Dario Andrea Bini and Bruno Iannazzo",
  title =        "A note on computing matrix geometric means",
  journal =      j-ADV-COMPUT-MATH,
  volume =       "35",
  number =       "2--4",
  pages =        "175--192",
  month =        nov,
  year =         "2011",
  CODEN =        "ACMHEX",
  DOI =          "https://doi.org/10.1007/s10444-010-9165-0",
  ISSN =         "1019-7168 (print), 1572-9044 (electronic)",
  ISSN-L =       "1019-7168",
  MRclass =      "65F30 (15A15 15B48)",
  MRnumber =     "2827085",
  bibdate =      "Sat Feb 3 18:22:54 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/article/10.1007/s10444-010-9165-0",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Computational Mathematics",
  journal-URL =  "http://link.springer.com/journal/10444",
}

@Article{Carls:2011:GTC,
  author =       "Robert Carls",
  title =        "{Galois} Theory of the Canonical Theta Structure",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "173--202",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111003934",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111003934",
  abstract =     "In this article, we give a Galois-theoretic
                 characterization of the canonical theta structure. The
                 Galois property of the canonical theta structure
                 translates into certain $p$-adic theta relations which
                 are satisfied by the canonical theta null point of the
                 canonical lift. As an application, we prove some 2-adic
                 theta identities which describe the set of canonical
                 theta null points of the canonical lifts of ordinary
                 abelian varieties in characteristic 2. The latter theta
                 relations are suitable for explicit canonical lifting.
                 Using the theory of canonical theta null points, we are
                 able to give a theoretical foundation to Mestre's point
                 counting algorithm which is based on the computation of
                 the generalized arithmetic geometric mean sequence.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Casquilho:2011:MDA,
  author =       "Miguel Casquilho and Jorge Buescu",
  title =        "A minimum distance: arithmetic and harmonic means in a
                 geometric dispute",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "42",
  number =       "3",
  pages =        "399--405",
  year =         "2011",
  CODEN =        "IJMEBM",
  DOI =          "https://doi.org/10.1080/0020739X.2010.526253",
  ISSN =         "0020-739x (print), 1464-5211 (electronic)",
  ISSN-L =       "0020-739X",
  MRclass =      "26E60 (51M16)",
  MRnumber =     "2787160",
  MRreviewer =   "Yu Dong Wu",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  journal-URL =  "http://www.tandfonline.com/loi/tmes20",
}

@Article{Chu:2011:OCC,
  author =       "Yu-Ming Chu and Cheng Zong and Gen-Di Wang",
  title =        "Optimal convex combination bounds of {Seiffert} and
                 geometric means for the arithmetic mean",
  journal =      j-J-MATH-INEQUAL,
  volume =       "5",
  number =       "3",
  pages =        "429--434",
  year =         "2011",
  DOI =          "https://doi.org/10.7153/jmi-05-37",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "26E60 (26D07)",
  MRnumber =     "2865559",
  MRreviewer =   "P{\'a}l Burai",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Chu:2011:OIB,
  author =       "Yu-Ming Chu and Miao-Kun Wang",
  title =        "Optimal inequalities between harmonic, geometric,
                 logarithmic, and arithmetic--geometric means",
  journal =      j-J-APPL-MATH,
  pages =        "618929:1--618929:9",
  year =         "2011",
  DOI =          "https://doi.org/10.1155/2011/618929",
  ISSN =         "1110-757x (print), 1687-0042 (electronic)",
  ISSN-L =       "1110-757X",
  MRclass =      "26E60",
  MRnumber =     "2846444",
  MRreviewer =   "Raghib M. Abu-Saris",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Mathematics",
  journal-URL =  "http://www.hindawi.com/journals/jam/",
}

@Article{Dupont:2011:FEM,
  author =       "R{\'e}gis Dupont",
  title =        "Fast evaluation of modular functions using {Newton}
                 iterations and the {AGM}",
  journal =      j-MATH-COMPUT,
  volume =       "80",
  number =       "275",
  pages =        "1823--1847",
  month =        jul,
  year =         "2011",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-2011-01880-6",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Apr 18 06:32:30 MDT 2011",
  bibsource =    "http://www.ams.org/mcom/2011-80-275;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-01880-6/;
                 http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-01880-6/S0025-5718-2011-01880-6.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Freour:2011:MCS,
  author =       "S. Fr{\'e}our and E. Lacoste and J. Fajoui and F.
                 Jacquemin",
  title =        "On the meaning of the chosen set-averaging method
                 within {Eshelby--Kr{\"o}ner} self-consistent scale
                 transition model: the geometric mean versus the
                 classical arithmetic average",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "91",
  number =       "9",
  pages =        "689--698",
  year =         "2011",
  CODEN =        "ZAMMAX",
  DOI =          "https://doi.org/10.1002/zamm.201000167",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  MRclass =      "74Q20",
  MRnumber =     "2838542",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ZAMM. Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik. Journal of Applied Mathematics and
                 Mechanics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
}

@Book{Gauss:2011:W,
  author =       "Carl Friedrich Gauss",
  title =        "Werke",
  volume =       "3",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "514",
  year =         "2011",
  DOI =          "https://doi.org/10.1017/CBO9781139058247",
  ISBN =         "1-108-03225-7 (paperback), 1-139-05824-X (e-book)",
  ISBN-13 =      "978-1-108-03225-4 (paperback), 978-1-139-05824-7
                 (e-book)",
  LCCN =         "????",
  bibdate =      "Tue Mar 14 18:59:37 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "Cambridge library collection. Mathematics",
  abstract =     "The genius of Carl Friedrich Gauss (1777-1855) and the
                 novelty of his work (published in Latin, German, and
                 occasionally French) in areas as diverse as number
                 theory, probability and astronomy were already widely
                 acknowledged during his lifetime. But it took another
                 three generations of mathematicians to reveal the true
                 extent of his output as they studied Gauss' extensive
                 unpublished papers and his voluminous correspondence.
                 This posthumous twelve-volume collection of Gauss'
                 complete works, published between 1863 and 1933, marks
                 the culmination of their efforts and provides a
                 fascinating account of one of the great scientific
                 minds of the nineteenth century. Volume 3, which
                 appeared in 1866, focuses on analysis. It includes
                 Gauss' work on elliptic functions and on power series,
                 for which he gave the first convergence criteria, as
                 well as his first (1799) proof of the fundamental
                 theorem of algebra, and reviews of works by
                 contemporaries including Fourier.",
  acknowledgement = ack-nhfb,
  author-dates = "1777--1855",
  remark =       "Originally published in G{\"o}ttingen: Koniglichen
                 Gesellschaft der Wissenschaften, 1866",
}

@Article{Gumus:2011:SVI,
  author =       "Ibrahim Halil Gumus and Omar Hirzallah and Necati
                 Taskara",
  title =        "Singular value inequalities for the arithmetic,
                 geometric and {Heinz} means of matrices",
  journal =      j-LIN-MULT-ALGEBRA,
  volume =       "59",
  number =       "12",
  pages =        "1383--1392",
  year =         "2011",
  CODEN =        "LNMLAZ",
  DOI =          "https://doi.org/10.1080/03081087.2011.556632",
  ISSN =         "0308-1087 (print), 1563-5139 (electronic)",
  ISSN-L =       "0308-1087",
  MRclass =      "15A42 (15A45 15B48)",
  MRnumber =     "2855842",
  MRreviewer =   "Yonghui Liu",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear and Multilinear Algebra",
  journal-URL =  "http://www.tandfonline.com/loi/glma20",
}

@Article{Kim:2011:MGM,
  author =       "Sejong Kim and Jimmie Lawson and Yongdo Lim",
  title =        "The matrix geometric mean of parameterized, weighted
                 arithmetic and harmonic means",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "435",
  number =       "9",
  pages =        "2114--2131",
  day =          "1",
  month =        nov,
  year =         "2011",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2011.04.010",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15B48 (47A64)",
  MRnumber =     "2810556",
  MRreviewer =   "T. Ando",
  bibdate =      "Mon Jun 13 18:34:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.sciencedirect.com/science/journal/00243795",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Lecko:2011:DSA,
  author =       "A. Lecko and M. Lecko",
  title =        "Differential subordinations of arithmetic and
                 geometric means of some functionals related to a
                 sector",
  journal =      j-INT-J-MATH-MATH-SCI,
  pages =        "205845:1--205845:19",
  year =         "2011",
  DOI =          "https://doi.org/10.1155/2011/205845",
  ISSN =         "0161-1712 (print), 1687-0425 (electronic)",
  ISSN-L =       "0161-1712",
  MRclass =      "30C80 (30C45)",
  MRnumber =     "2799845",
  MRreviewer =   "Roger W. Barnard",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
  journal-URL =  "https://www.hindawi.com/journals/ijmms/",
}

@Article{Long:2011:OGL,
  author =       "Bo-Yong Long and Yu-Ming Chu",
  title =        "Optimal generalized logarithmic mean bounds for the
                 geometric combination of arithmetic and harmonic
                 means",
  journal =      "J. Indones. Math. Soc.",
  volume =       "17",
  number =       "2",
  pages =        "85--96",
  year =         "2011",
  DOI =          "https://doi.org/10.22342/jims.17.2.5.85-95",
  ISSN =         "2086-8952",
  MRclass =      "26E60",
  MRnumber =     "2919042",
  MRreviewer =   "M. Hajja",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Indonesian Mathematical Society",
}

@Article{Molnar:2011:CMM,
  author =       "Lajos Moln{\'a}r",
  title =        "Continuous maps on matrices transforming geometric
                 mean to arithmetic mean",
  journal =      "Ann. Univ. Sci. Budapest. Sect. Comput.",
  volume =       "35",
  pages =        "217--222",
  year =         "2011",
  ISSN =         "0138-9491",
  MRclass =      "47B49 (47A64)",
  MRnumber =     "2894562",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annales Universitatis Scientiarum Budapestinensis de
                 Rolando E{\"o}tv{\"o}s Nominatae. Sectio
                 Computatorica",
}

@Article{Shirali:2011:BPG,
  author =       "Shailesh A. Shirali",
  title =        "95.09 {A} bootstrapping proof of the {AM--GM}
                 Inequality for three variables",
  journal =      j-MATH-GAZ,
  volume =       "95",
  number =       "532",
  pages =        "86--87",
  month =        mar,
  year =         "2011",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.1017/S0025557200002412",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Tue May 5 12:04:14 MDT 2015",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=MAG&volumeId=95&issueId=532;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayBackIssues?jid=MAG",
}

@Article{Wang:2011:SDI,
  author =       "Miao-Kun Wang and Yu-Ming Chu and Gen-Di Wang",
  title =        "A Sharp Double Inequality Between the {Lehmer} and
                 Arithmetic--Geometric Means",
  journal =      j-PAC-J-APPL-MATH,
  volume =       "3",
  number =       "4",
  pages =        "281--286",
  month =        "????",
  year =         "2011",
  ISSN =         "1941-3963",
  MRclass =      "26E60",
  MRnumber =     "3024759",
  bibdate =      "Wed Mar 15 07:14:39 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "https://www.novapublishers.com/catalog/product_info.php?products_id=24770",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Applied Mathematics",
  journal-URL =  "http://www.novapublishers.com/catalog/product_info.php?products_id=6697",
}

@Article{Zhang:2011:IGM,
  author =       "Qian Zhang and Bing Xu",
  title =        "An invariance of geometric mean with respect to
                 generalized quasi-arithmetic means",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "379",
  number =       "1",
  pages =        "65--74",
  year =         "2011",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/j.jmaa.2010.12.025",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "26E60 (34A05)",
  MRnumber =     "2776455",
  MRreviewer =   "Alan L. Horwitz",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
}

@Article{Albadawi:2012:SVA,
  author =       "Hussien Albadawi",
  title =        "Singular value and arithmetic--geometric mean
                 inequalities for operators",
  journal =      j-ANN-FUNCT-ANAL,
  volume =       "3",
  number =       "1",
  pages =        "10--18",
  year =         "2012",
  DOI =          "https://doi.org/10.15352/afa/1399900020",
  ISSN =         "2008-8752",
  MRclass =      "47A30",
  MRnumber =     "2903264",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Functional Analysis",
  journal-URL =  "http://projecteuclid.org/afa",
}

@Article{Aldaz:2012:SBD,
  author =       "J. M. Aldaz",
  title =        "Sharp bounds for the difference between the arithmetic
                 and geometric means",
  journal =      "Arch. Math. (Basel)",
  volume =       "99",
  number =       "4",
  pages =        "393--399",
  year =         "2012",
  DOI =          "https://doi.org/10.1007/s00013-012-0434-7",
  ISSN =         "0003-889x (print), 1420-8938 (electronic)",
  MRclass =      "26E60 (26D15 60E15)",
  MRnumber =     "2990158",
  MRreviewer =   "Huan Nan Shi",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Archiv der Mathematik",
}

@Article{Barratt:2012:IPC,
  author =       "Carl Barratt and Ramesh Sharma",
  title =        "96.16 {An} inductive proof of the condition for the
                 {AM--GM} equality",
  journal =      j-MATH-GAZ,
  volume =       "96",
  number =       "535",
  pages =        "131--133",
  month =        mar,
  year =         "2012",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.1017/S0025557200004162",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Tue May 5 12:04:21 MDT 2015",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=MAG&volumeId=96&issueId=535;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayBackIssues?jid=MAG",
}

@Article{Chu:2012:IBA,
  author =       "Yu-Ming Chu and Miao-Kun Wang",
  title =        "Inequalities between arithmetic--geometric, {Gini},
                 and {Toader} means",
  journal =      j-ABSTR-APPL-ANAL,
  pages =        "830585:1--830585:11",
  year =         "2012",
  DOI =          "https://doi.org/10.1155/2012/830585",
  ISSN =         "1085-3375 (print), 1687-0409 (electronic)",
  ISSN-L =       "1085-3375",
  MRclass =      "26E60 (26D20)",
  MRnumber =     "2861493",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Abstract and Applied Analysis",
}

@Article{Chu:2012:OLM,
  author =       "Y.-M. Chu and M.-K. Wang and Y.-F. Qiu",
  title =        "Optimal {Lehmer} mean bounds for the geometric and
                 arithmetic combinations of arithmetic and {Seiffert}
                 means",
  journal =      "Azerb. J. Math.",
  volume =       "2",
  number =       "1",
  pages =        "3--9",
  year =         "2012",
  ISSN =         "2218-6816",
  MRclass =      "26E60 (26D99)",
  MRnumber =     "2967278",
  MRreviewer =   "P{\'a}l Burai",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Azerbaijan Journal of Mathematics",
}

@Article{Chung:2012:VAG,
  author =       "Kun-Jen Chung",
  title =        "On the validity of the arithmetic--geometric mean
                 method to locate the optimal solution in a supply chain
                 system",
  journal =      j-INT-J-SYST-SCI,
  volume =       "43",
  number =       "8",
  pages =        "1454--1463",
  year =         "2012",
  CODEN =        "IJSYA9",
  DOI =          "https://doi.org/10.1080/00207721.2010.547628",
  ISSN =         "0020-7721 (print), 1464-5319 (electronic)",
  ISSN-L =       "0020-7721",
  MRclass =      "90B05",
  MRnumber =     "2946981",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Systems Science. Principles
                 and Applications of Systems and Integration",
  journal-URL =  "http://www.tandfonline.com/loi/tsys20",
}

@Article{Friedrich:2012:RGM,
  author =       "Jan O. Friedrich and Neill K. J. Adhikari and Joseph
                 Beyene",
  title =        "Ratio of geometric means to analyze continuous
                 outcomes in meta-analysis: comparison to mean
                 differences and ratio of arithmetic means using empiric
                 data and simulation",
  journal =      "Stat. Med.",
  volume =       "31",
  number =       "17",
  pages =        "1857--1886",
  year =         "2012",
  DOI =          "https://doi.org/10.1002/sim.4501",
  ISSN =         "0277-6715",
  MRclass =      "Expansion",
  MRnumber =     "2956005",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics in Medicine",
}

@Article{Gong:2012:SDI,
  author =       "Wei-Ming Gong and Ying-Qing Song and Miao-Kun Wang and
                 Yu-Ming Chu",
  title =        "A sharp double inequality between {Seiffert},
                 arithmetic, and geometric means",
  journal =      j-ABSTR-APPL-ANAL,
  pages =        "684834:1--684834:7",
  year =         "2012",
  ISSN =         "1085-3375 (print), 1687-0409 (electronic)",
  ISSN-L =       "1085-3375",
  MRclass =      "26E60 (26D07)",
  MRnumber =     "2965473",
  MRreviewer =   "Raghib M. Abu-Saris",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Abstract and Applied Analysis",
}

@Article{Hadjidimos:2012:IEO,
  author =       "Apostolos Hadjidimos",
  title =        "Irreducibility and extensions of {Ostrowski's
                 Theorem}",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "436",
  number =       "7",
  pages =        "2156--2168",
  year =         "2012",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2011.11.035",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379511007786",
  abstract =     "In this paper an extension of Ostrowski's Theorem for
                 complex square irreducible matrices is presented. Also
                 extensions of similar statements for square complex
                 matrices are analyzed and completed. Most of the
                 statements in this work cover also the case of
                 reducible matrices.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Alpha-matrices; Ostrowski's Theorems; H{\"o}lder
                 inequality; (irreducibly) diagonally dominant matrices;
                 Generalized arithmetic--geometric mean inequality",
}

@Article{He:2012:IAG,
  author =       "Chuanjiang He and Limin Zou and Shahid Qaisar",
  title =        "On improved arithmetic--geometric mean and {Heinz}
                 inequalities for matrices",
  journal =      j-J-MATH-INEQUAL,
  volume =       "6",
  number =       "3",
  pages =        "453--459",
  year =         "2012",
  DOI =          "https://doi.org/10.7153/jmi-06-42",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "15A42 (15A18 15A60)",
  MRnumber =     "3012207",
  MRreviewer =   "Jaspal Singh Aujla",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{He:2012:OIB,
  author =       "Zai-Yin He and Yu-Ming Chu",
  title =        "Optimal inequalities between one-parameter mean and
                 the combination of arithmetic, geometric and harmonic
                 means",
  journal =      j-PAC-J-APPL-MATH,
  volume =       "4",
  number =       "3",
  pages =        "149--154",
  year =         "2012",
  ISSN =         "1941-3963",
  MRclass =      "26E60",
  MRnumber =     "3060210",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Applied Mathematics",
  journal-URL =  "http://www.novapublishers.com/catalog/product_info.php?products_id=6697",
}

@Article{Kinjo:2012:HSA,
  author =       "Kensaku Kinjo and Yuken Miyasaka",
  title =        "Hypergeometric series and arithmetic--geometric mean
                 over $2$-adic fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "8",
  number =       "3",
  pages =        "831--844",
  month =        may,
  year =         "2012",
  DOI =          "https://doi.org/10.1142/S1793042112500480",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  MRclass =      "11S80 (11G20 33C05)",
  MRnumber =     "2904934",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042112500480",
  abstract =     "Dwork proved that the Gaussian hypergeometric function
                 on $p$-adic numbers can be extended to a function which
                 takes values of the unit roots of ordinary elliptic
                 curves over a finite field of characteristic $ p \geq
                 3$. We present an analogous theory in the case $ p =
                 2$. As an application, we give a relation between the
                 canonical lift and the unit root of an elliptic curve
                 over a finite field of characteristic $2$ by using the
                 $2$-adic arithmetic--geometric mean.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kittaneh:2012:IAG,
  author =       "Fuad Kittaneh and Mario Krni{\'c} and Neda
                 Lovri{\v{c}}evi{\'c} and Josip Pe{\v{c}}ari{\'c}",
  title =        "Improved arithmetic--geometric and {Heinz} means
                 inequalities for {Hilbert} space operators",
  journal =      j-PUBL-MATH-DEBRECEN,
  volume =       "80",
  number =       "3-4",
  pages =        "465--478",
  year =         "2012",
  CODEN =        "PUMAAR",
  DOI =          "https://doi.org/10.5486/PMD.2012.5193",
  ISSN =         "0033-3883 (print), 2064-2849 (electronic)",
  MRclass =      "47A63 (26D10 26E60)",
  MRnumber =     "2943018",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Publicationes Mathematicae Debrecen",
  journal-URL =  "http://publi.math.unideb.hu/",
}

@Article{Kum:2012:GMP,
  author =       "Sangho Kum and Yongdo Lim",
  title =        "A geometric mean of parameterized arithmetic and
                 harmonic means of convex functions",
  journal =      j-ABSTR-APPL-ANAL,
  pages =        "836804:1--836804:15",
  year =         "2012",
  ISSN =         "1085-3375 (print), 1687-0409 (electronic)",
  ISSN-L =       "1085-3375",
  MRclass =      "26E60 (26B25)",
  MRnumber =     "3004919",
  MRreviewer =   "Silvia Toader",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Abstract and Applied Analysis",
}

@Article{Maligranda:2012:GIE,
  author =       "Lech Maligranda",
  title =        "The {AM--GM} Inequality is Equivalent to the
                 {Bernoulli} Inequality",
  journal =      j-MATH-INTEL,
  volume =       "34",
  number =       "1",
  pages =        "1--2",
  month =        "????",
  year =         "2012",
  CODEN =        "MAINDC",
  DOI =          "https://doi.org/10.1007/s00283-011-9266-8",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  bibdate =      "Thu Feb 14 06:39:03 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Intelligencer",
  journal-URL =  "http://link.springer.com/journal/283",
  keywords =     "AM (arithmetic mean); GM (geometric mean)",
  remark =       "This paper references two books that provide 52 and 74
                 proofs of the {\em Cauchy inequality\/} (1821), {$ {\rm
                 AM} \geq {\rm GM} $}, and gives a short proof that it
                 and the {\em Barrow--Bernoulli inequality} (1670,
                 1689), $ x^n \geq 1 + n(x - 1) $, for any $ x > 0 $ and
                 $n$ an integer, are mutually equivalent: either one
                 implies the other.",
}

@Article{Maze:2012:NWH,
  author =       "G{\'e}rard Maze and Urs Wagner",
  title =        "A note on the weighted harmonic--geometric--arithmetic
                 means inequalities",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "15",
  number =       "1",
  pages =        "15--26",
  year =         "2012",
  DOI =          "https://doi.org/10.7153/mia-15-02",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "26D15 (15A42 26E60)",
  MRnumber =     "2919427",
  MRreviewer =   "Alfred Witkowski",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Seo:2012:AGM,
  author =       "Yuki Seo",
  title =        "The arithmetic--geometric mean inequality in an
                 external formula",
  journal =      j-SCI-MATH-JPN,
  volume =       "75",
  number =       "3",
  pages =        "299--305",
  year =         "2012",
  ISSN =         "1346-0862",
  ISSN-L =       "1346-0447",
  MRclass =      "47A63 (26D10)",
  MRnumber =     "3099760",
  MRreviewer =   "T. Ando",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientiae Mathematicae Japonicae",
  journal-URL =  "http://www.jams.or.jp/notice/scmj/smj.html",
}

@Article{Spandaw:2012:HIG,
  author =       "Jeroen Spandaw and Duco van Straten",
  title =        "Hyperelliptic integrals and generalized
                 arithmetic--geometric mean",
  journal =      j-RAMANUJAN-J,
  volume =       "28",
  number =       "1",
  pages =        "61--78",
  year =         "2012",
  CODEN =        "RAJOF9",
  DOI =          "https://doi.org/10.1007/s11139-011-9353-7",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  MRclass =      "14K25 (14H40)",
  MRnumber =     "2914453",
  MRreviewer =   "Ahmed Lesfari",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Ramanujan Journal. An International Journal Devoted to
                 the Areas of Mathematics Influenced by Ramanujan",
  journal-URL =  "http://link.springer.com/journal/11139",
}

@Article{Wang:2012:SDI,
  author =       "Miao-Kun Wang and Yu-Ming Chu and Gen-Di Wang",
  title =        "A Sharp Double Inequality Between the {Lehmer} and
                 Arithmetic--Geometric Means",
  journal =      j-PAC-J-APPL-MATH,
  volume =       "4",
  number =       "1",
  pages =        "1--25",
  year =         "2012",
  ISSN =         "1941-3963",
  MRclass =      "26E60 (26D07)",
  MRnumber =     "3027346",
  bibdate =      "Wed Mar 15 07:16:27 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Applied Mathematics",
  journal-URL =  "http://www.novapublishers.com/catalog/product_info.php?products_id=6697",
}

@Article{Xia:2012:OOP,
  author =       "Weifeng Xia and Shouwei Hou and Gendi Wang and Yuming
                 Chu",
  title =        "Optimal one-parameter mean bounds for the convex
                 combination of arithmetic and geometric means",
  journal =      "J. Appl. Anal.",
  volume =       "18",
  number =       "2",
  pages =        "197--207",
  year =         "2012",
  DOI =          "https://doi.org/10.1515/jaa-2012-0013",
  ISSN =         "1425-6908",
  MRclass =      "26E60 (26D20)",
  MRnumber =     "2999377",
  MRreviewer =   "Huan Nan Shi",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Analysis",
}

@Article{Baricz:2013:TTI,
  author =       "{\'A}rp{\'a}d Baricz and Kondooru Raghavendar and
                 Anbhu Swaminathan",
  title =        "{Tur{\'a}n} type inequalities for $q$-hypergeometric
                 functions",
  journal =      j-J-APPROX-THEORY,
  volume =       "168",
  number =       "??",
  pages =        "69--79",
  year =         "2013",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1016/j.jat.2013.01.002",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021904513000129",
  abstract =     "In this paper our aim is to deduce some Tur{\'a}n type
                 inequalities for $q$-hypergeometric and $q$-confluent
                 hypergeometric functions. In order to obtain the main
                 results we apply the methods developed in the case of
                 classical Kummer and Gauss hypergeometric functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  keywords =     "Arithmetic, geometric mean; Basic hypergeometric
                 functions; Gauss and Kummer hypergeometric functions; q
                 -Kummer confluent hypergeometric functions; Tur{\'a}n
                 type inequalities",
}

@Article{Chu:2013:IAG,
  author =       "Yu Ming Chu and Miao Kun Wang",
  title =        "Inequalities among generalized logarithmic, arithmetic
                 and geometric means",
  journal =      "Acta Math. Sci. Ser. A Chin. Ed.",
  volume =       "33",
  number =       "2",
  pages =        "298--308",
  year =         "2013",
  ISSN =         "1003-3998",
  MRclass =      "26E60 (26D20 41A44)",
  MRnumber =     "3088293",
  MRreviewer =   "Huan Nan Shi",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Mathematica Scientia. Series A. Shuxue Wuli
                 Xuebao. Chinese Edition",
}

@Article{Chu:2013:STP,
  author =       "Yu-Ming Chu and Miao-Kun Wang and Ye-Fang Qiu and
                 Xiao-Yan Ma",
  title =        "Sharp two parameter bounds for the logarithmic mean
                 and the arithmetic--geometric mean of {Gauss}",
  journal =      j-J-MATH-INEQUAL,
  volume =       "7",
  number =       "3",
  pages =        "349--355",
  year =         "2013",
  DOI =          "https://doi.org/10.7153/jmi-07-31",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "26E60",
  MRnumber =     "3115070",
  MRreviewer =   "Biljana P. Mihailovi{\'c}",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Cremona:2013:CAPa,
  author =       "John E. Cremona and Thotsaphon Thongjunthug",
  title =        "The complex {AGM}, periods of elliptic curves over and
                 complex elliptic logarithms",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--32",
  day =          "20",
  month =        feb,
  year =         "2013",
  bibdate =      "Tue Mar 14 18:14:33 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "https://arxiv.org/pdf/1011.0914.pdf",
  abstract =     "We give an account of the complex
                 Arithmetic--Geometric Mean (AGM), as first studied by
                 Gauss, together with details of its relationship with
                 the theory of elliptic curves over $C$, their period
                 lattices and complex parametrisation. As an
                 application, we present efficient methods for computing
                 bases for the period lattices and elliptic logarithms
                 of points, for arbitrary elliptic curves defined over
                 $C$. Earlier authors have only treated the case of
                 elliptic curves defined over the real numbers; here,
                 the multi-valued nature of the complex AGM plays an
                 important role. Our method, which we have implemented
                 in both MAGMA and Sage, is illustrated with several
                 examples using elliptic curves defined over number
                 fields with real and complex embeddings.",
  acknowledgement = ack-nhfb,
}

@Article{Cremona:2013:CAPb,
  author =       "John E. Cremona and Thotsaphon Thongjunthug",
  title =        "The complex {AGM}, periods of elliptic curves over {$
                 \mathbb {C} $} and complex elliptic logarithms",
  journal =      j-J-NUMBER-THEORY,
  volume =       "133",
  number =       "8",
  pages =        "2813--2841",
  month =        aug,
  year =         "2013",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2013.02.002",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X13000735",
  abstract =     "We give an account of the complex
                 Arithmetic--Geometric Mean (AGM), as first studied by
                 Gauss, together with details of its relationship with
                 the theory of elliptic curves over $C$, their period
                 lattices and complex parametrisation. As an
                 application, we present efficient methods for computing
                 bases for the period lattices and elliptic logarithms
                 of points, for arbitrary elliptic curves defined over
                 $C$. Earlier authors have only treated the case of
                 elliptic curves defined over the real numbers; here,
                 the multi-valued nature of the complex AGM plays an
                 important role. Our method, which we have implemented
                 in both MAGMA and Sage, is illustrated with several
                 examples using elliptic curves defined over number
                 fields with real and complex embeddings.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
  keywords =     "Arithmetic--geometric mean; Elliptic curve; Elliptic
                 logarithm; Period lattice",
}

@Article{Crisan:2013:DSI,
  author =       "O. Cri{\c{s}}an and S. Kanas",
  title =        "Differential subordinations involving arithmetic and
                 geometric means",
  journal =      j-APPL-MATH-COMP,
  volume =       "222",
  number =       "??",
  pages =        "123--131",
  day =          "1",
  month =        oct,
  year =         "2013",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2013.07.051",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "30C45 (30C80)",
  MRnumber =     "3115856",
  bibdate =      "Mon Dec 2 12:34:37 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300313008011",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Gumus:2013:IAG,
  author =       "I. Halil Gumus and Necati Taskara",
  title =        "The improved arithmetic--geometric mean inequalities
                 for matrix norms",
  journal =      j-APPL-MATH-SCI-RUSE,
  volume =       "7",
  number =       "29--32",
  pages =        "1439--1446",
  year =         "2013",
  DOI =          "https://doi.org/10.12988/ams.2013.13132",
  ISSN =         "1312-885x (print), 1314-7552 (electronic)",
  MRclass =      "26D15",
  MRnumber =     "3021302",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematical Sciences",
  journal-URL =  "http://www.m-hikari.com/ams/",
}

@Article{Hassani:2013:AGM,
  author =       "Mehdi Hassani",
  title =        "On the arithmetic--geometric mean inequality",
  journal =      j-TAMKANG-J-MATH,
  volume =       "44",
  number =       "4",
  pages =        "453--456",
  year =         "2013",
  DOI =          "https://doi.org/10.5556/j.tkjm.44.2013.1418",
  ISSN =         "0049-2930 (print), 2073-9826 (electronic)",
  ISSN-L =       "2073-9826",
  MRclass =      "26D15",
  MRnumber =     "3153080",
  MRreviewer =   "M. E. Muldoon",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tamkang Journal of Mathematics",
  journal-URL =  "http://journals.math.tku.edu.tw/index.php/TKJM",
}

@Article{Hassani:2013:RAG,
  author =       "Mehdi Hassani",
  title =        "On the ratio of the arithmetic and geometric means of
                 the prime numbers and the number $e$",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "9",
  number =       "6",
  pages =        "1593--1603",
  month =        sep,
  year =         "2013",
  DOI =          "https://doi.org/10.1142/S1793042113500450",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  MRclass =      "11N05 (11N56)",
  MRnumber =     "3103906",
  MRreviewer =   "Daniel Fiorilli",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042113500450",
  abstract =     "We study the asymptotic behavior of the sequence with
                 general term consisting of the ratio $ A_n $ by $ G_n
                 $, the arithmetic and geometric means of the prime
                 numbers $ p_1 $, $ p_2 $, \ldots, $ p_n $,
                 respectively, in which, $ p_n $ denotes the $n$-th
                 prime number.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@InCollection{Kinjo:2013:HSA,
  author =       "Kensaku Kinjo and Yuken Miyasaka",
  booktitle =    "Algebraic number theory and related topics 2011",
  title =        "Hypergeometric series and arithmetic--geometric mean
                 over 2-adic fields",
  publisher =    "Res. Inst. Math. Sci. (RIMS), Kyoto",
  pages =        "99--110",
  year =         "2013",
  MRclass =      "11G20 (33C05)",
  MRnumber =     "3221722",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "RIMS K{\^o}ky{\^u}roku Bessatsu, B44",
  acknowledgement = ack-nhfb,
}

@Article{Liu:2013:SBS,
  author =       "Baoyu Liu and Weiming Gong and Yingqing Song and
                 Yuming Chu",
  title =        "Sharp bounds for {Seiffert} mean in terms of
                 arithmetic and geometric means",
  journal =      "Int. J. Math. Anal. (Ruse)",
  volume =       "7",
  number =       "33-36",
  pages =        "1765--1773",
  year =         "2013",
  DOI =          "https://doi.org/10.12988/ijma.2013.3349",
  ISSN =         "1312-8876",
  MRclass =      "26E60",
  MRnumber =     "3066546",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Analysis",
}

@Article{Najafi:2013:SRK,
  author =       "Hamed Najafi",
  title =        "Some results on {Kwong} functions and related
                 inequalities",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "439",
  number =       "9",
  pages =        "2634--2641",
  year =         "2013",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2013.06.018",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379513004175",
  abstract =     "We investigate some relations between Kwong functions
                 and operator monotone functions. As an application, we
                 present an arithmetic--geometric mean type inequality
                 by showing that for two continuous functions $f$, $g$
                 on $ (0, \infty)$ such that $ h (t) = f (t) g (t)$ is a
                 Kwong function and $ f (t) g (t) \leq t$, any positive
                 matrices $A$, $B$ and any matrix $X$, it holds that $
                 ||| f (A) X g (B) + g (A) X f (B) ||| \leq ||| A X + X
                 B |||$ for each unitarily invariant norm $ ||| \cdot
                 |||$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Arithmetic--geometric mean type inequality; Kwong
                 function; Operator monotone function",
}

@Article{Ouyang:2013:OPL,
  author =       "Liang-Yuh Ouyang and Chun-Tao Chang",
  title =        "Optimal production lot with imperfect production
                 process under permissible delay in payments and
                 complete backlogging",
  journal =      j-INT-J-PROD-ECON,
  volume =       "144",
  number =       "2",
  pages =        "610--617",
  year =         "2013",
  CODEN =        "JPCEYE",
  DOI =          "https://doi.org/10.1016/j.ijpe.2013.04.027",
  ISSN =         "0925-5273 (print), 1873-7579 (electronic)",
  ISSN-L =       "0925-5273",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0925527313001916",
  abstract =     "The traditional economic production quantity (EPQ)
                 model assumes that the production products are all
                 perfect. It is not always true in the real production
                 system, due to imperfect production process or other
                 factors, imperfect quality items may be produced.
                 Furthermore, it is well-known that the total
                 production-inventory costs can be reduced by reworking
                 the imperfect quality items produced with a relatively
                 smaller additional reworking and holding costs. In
                 addition, the permissible delay in payments offered by
                 the supplier is widely adopted in the practical
                 business market. In this study, we explore the effects
                 of the reworking imperfect quality items and trade
                 credit on the EPQ model with imperfect production
                 processes and complete backlogging. A mathematical
                 model which includes the reworking and shortage costs,
                 interest earned and interest charged is presented.
                 Besides, an arithmetic--geometric mean inequality
                 approach is employed and an algorithm is developed to
                 find the optimal production policy. Furthermore, some
                 numerical examples and sensitivity analysis are
                 provided to demonstrate the proposed model.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Production Economics",
  keywords =     "Arithmetic--geometric mean inequality; Complete
                 backlogging; Imperfect production process; Inventory;
                 Permissible delay in payments",
}

@Article{Shao:2013:SRI,
  author =       "Zhi Hua Shao and Xiao Ming Zhang",
  title =        "Some results involving upper and lower bounds for the
                 difference of arithmetic mean and geometric mean",
  journal =      "Math. Pract. Theory",
  volume =       "43",
  number =       "6",
  pages =        "206--214",
  year =         "2013",
  ISSN =         "1000-0984",
  MRclass =      "26E60",
  MRnumber =     "3114600",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics in Practice and Theory. Shuxue de Shijian
                 yu Renshi",
}

@Article{Xu:2013:PPM,
  author =       "Bai-Xiang Xu and Yang Gao and Min-Zhong Wang",
  title =        "Particle packing and the mean theory",
  journal =      j-PHYS-LET-A,
  volume =       "377",
  number =       "3--4",
  pages =        "145--147",
  year =         "2013",
  CODEN =        "PYLAAG",
  DOI =          "https://doi.org/10.1016/j.physleta.2012.11.022",
  ISSN =         "0375-9601 (print), 1873-2429 (electronic)",
  ISSN-L =       "0375-9601",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/kepler.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0375960112011772",
  abstract =     "This Letter presents two mean relations between the
                 densities/porosities of random and regular packing
                 modes. The two mean relations work very well for the
                 packing of spherical particles, cubic particles and
                 circular discs. Results confirm the corresponding
                 experimental and computational results.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Letters A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03759601",
  keywords =     "Arithmetic--geometric mean; Harmonic--geometric mean;
                 Packing density; Particle packing",
}

@Article{Yamazaki:2013:EPA,
  author =       "T. Yamazaki",
  title =        "An elementary proof of arithmetic--geometric mean
                 inequality of the weighted {Riemannian} mean of
                 positive definite matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "438",
  number =       "4",
  pages =        "1564--1569",
  day =          "15",
  month =        feb,
  year =         "2013",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2011.12.006",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15B48",
  MRnumber =     "3005242",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2010.bib",
  note =         "16th \{ILAS\} Conference Proceedings, Pisa 2010",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379511007865",
  abstract =     "The weighted Riemannian mean of positive definite
                 matrices is a kind of weighted geometric mean of n
                 matrices. Some properties of the weighted Riemannian
                 mean are easily obtained. But some of them are not
                 easy. In this short paper, a simplified proof of
                 arithmetic--geometric--harmonic mean inequalities will
                 be obtained.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
  keywords =     "Arithmetic--geometric mean inequality; Geometric mean;
                 Matrix inequality; Positive definite matrix; The
                 Riemannian mean",
}

@Article{Bellissima:2014:AGH,
  author =       "Fabio Bellissima",
  title =        "Arithmetic, geometric and harmonic means in music
                 theory",
  journal =      j-BOLL-STOR-SCI-MAT,
  volume =       "34",
  number =       "2",
  pages =        "201--244",
  year =         "2014",
  ISSN =         "0392-4432 (print), 1724-1650 (electronic)",
  ISSN-L =       "0392-4432",
  MRclass =      "00A65 (01A20 26E60)",
  MRnumber =     "3288578",
  MRreviewer =   "David Warren Bulger",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bollettino di Storia delle Scienze Matematiche",
}

@Article{Chang:2014:API,
  author =       "Hung-Chi Chang",
  title =        "An analysis of production-inventory models with
                 deteriorating items in a two-echelon supply chain",
  journal =      j-APPL-MATH-MODEL,
  volume =       "38",
  number =       "3",
  pages =        "1187--1191",
  year =         "2014",
  CODEN =        "AMMODL",
  DOI =          "https://doi.org/10.1016/j.apm.2013.07.031",
  ISSN =         "0307-904x (print), 1872-8480 (electronic)",
  ISSN-L =       "0307-904X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0307904X13004757",
  abstract =     "This paper revisits two previous studies that
                 addressed the integrated production--inventory problem
                 for deteriorating items in a two-echelon supply chain,
                 where the item's deterioration rate is a constant or
                 follows a continuous probability distribution function.
                 The aim of this study is to present an improved
                 solution procedure to determine the delivery lot size
                 and the number of deliveries per production batch cycle
                 that minimizes the total cost of the entire supply
                 chain. The performance of the proposed methodology is
                 illustrated analytically and numerically.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied mathematical modelling",
  keywords =     "Arithmetic--geometric mean method; Inventory; Marginal
                 analysis; Probabilistic deterioration; Supply chain",
}

@Article{Furuichi:2014:OIA,
  author =       "Shigeru Furuichi",
  title =        "Operator inequalities among arithmetic mean, geometric
                 mean and harmonic mean",
  journal =      j-J-MATH-INEQUAL,
  volume =       "8",
  number =       "3",
  pages =        "669--672",
  year =         "2014",
  DOI =          "https://doi.org/10.7153/jmi-08-49",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "47A05 (26E60)",
  MRnumber =     "3260334",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Hassani:2014:AGM,
  author =       "Mehdi Hassani",
  title =        "On the arithmetic--geometric means of positive
                 integers and the number $e$",
  journal =      "Appl. Math. E-Notes",
  volume =       "14",
  pages =        "250--255",
  year =         "2014",
  ISSN =         "1607-2510",
  MRclass =      "26E60",
  MRnumber =     "3324424",
  MRreviewer =   "Bing Xu",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics E-Notes",
}

@Article{Jameson:2014:AAG,
  author =       "G. J. O. Jameson",
  title =        "An approximation to the arithmetic--geometric mean",
  journal =      j-MATH-GAZ,
  volume =       "98",
  number =       "541",
  pages =        "85--95",
  month =        mar,
  year =         "2014",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.2307/3621497",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Tue May 5 12:04:31 MDT 2015",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=MAG&volumeId=98&issueId=541;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgazette2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  doi-bad =      "https://doi.org/10.2307/3621497",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayBackIssues?jid=MAG",
}

@Article{Osler:2014:RFR,
  author =       "Thomas J. Osler and Tirupathi R. Chandrupatla",
  title =        "98.23 Recursive formulas related to the
                 {Arithmetic--Geometric Mean}",
  journal =      j-MATH-GAZ,
  volume =       "98",
  number =       "543",
  pages =        "484--486",
  month =        nov,
  year =         "2014",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.1017/S0025557200008202",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Tue Nov 17 09:58:03 MST 2015",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=MAG&volumeId=98&issueId=543;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayBackIssues?jid=MAG",
}

@Article{Qian:2014:OBN,
  author =       "Wei-Mao Qian and Yu-Ming Chu",
  title =        "Optimal bounds for {Neuman} means in terms of
                 geometric, arithmetic and quadratic means",
  journal =      j-J-INEQUAL-APPL,
  pages =        "175:1--175:13",
  year =         "2014",
  DOI =          "https://doi.org/10.1186/1029-242X-2014-175",
  ISSN =         "1029-242X",
  MRclass =      "26E60",
  MRnumber =     "3346843",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Inequalities and Applications",
  journal-URL =  "http://journalofinequalitiesandapplications.springeropen.com/",
}

@Article{Srivastava:2014:ICE,
  author =       "H. M. Srivastava and N. Magesh and J. Yamini",
  title =        "Initial coefficient estimates for bi-$ \lambda
                 $-convex and bi-$ \mu $-starlike functions connected
                 with arithmetic and geometric means",
  journal =      "Electron. J. Math. Anal. Appl.",
  volume =       "2",
  number =       "2",
  pages =        "152--162",
  year =         "2014",
  ISSN =         "2090-729X",
  MRclass =      "30C45 (30C50)",
  MRnumber =     "3311256",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Journal of Mathematical Analysis and
                 Applications. EJMAA",
}

@Article{Villarino:2014:ASP,
  author =       "Mark B. Villarino",
  title =        "The {AGM} Simple Pendulum",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--19",
  day =          "1",
  month =        sep,
  year =         "2014",
  bibdate =      "Tue Mar 14 18:11:41 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "https://arxiv.org/pdf/1202.2782.pdf",
  abstract =     "We present a self-contained development of Gauss'
                 Arithmetic--Geometric Mean (AGM) and the work of the
                 great British number theorist A. E. Ingham who obtained
                 rigorous error bounds for the AGM's approximations to
                 the period of a simple pendulum. Moreover we discuss
                 the relation of complex multiplication to the AGM.",
  acknowledgement = ack-nhfb,
  remark =       "From page 2: ``It is unfortunate that none of the
                 authors [\cite{Carvalhaes:2008:APS} and Alfred George
                 Greenhill \booktitle{The Applications of Elliptic
                 Functions} (1892, 1959)] cites the marvelous
                 investigations of the great British number theorist A.
                 E. [Albert Edward] Ingham [(1900--1967)] which L. A.
                 Pars describes in his monumental 665-page standard work
                 \cite{Pars:1965:TAD,Pars:1968:TAD,Pars:1979:TAD}, which
                 was published almost 50 years ago in 1965. Ingham not
                 only obtains the formulas of Carvalhaes and Suppes
                 [\cite{Carvalhaes:2008:APS}] but also obtains rigorous
                 error estimates, both in excess and in defect. It is
                 beyond question that Ingham's work deserves to be
                 better known.'' [I cannot spot
                 elliptic-function-related work by Ingham in the 28
                 entries found in the MathSciNet database.]",
}

@Article{Wang:2014:BPE,
  author =       "Miao-Kun Wang and Yu-Ming Chu and Yue-Ping Jiang and
                 Song-Liang Qiu",
  title =        "Bounds of the perimeter of an ellipse using
                 arithmetic, geometric and harmonic means",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "17",
  number =       "1",
  pages =        "101--111",
  year =         "2014",
  DOI =          "https://doi.org/10.7153/mia-17-07",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "33E05 (26E60)",
  MRnumber =     "3220978",
  MRreviewer =   "Mehdi Hassani",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Wang:2014:NSC,
  author =       "Hua Wang and Tie-Hong Zhao and Ying-Qing Song and
                 Yu-Ming Chu",
  title =        "Necessary and sufficient conditions for inequalities
                 between the generalized {Muirhead} mean and arithmetic,
                 harmonic and geometric means",
  journal =      j-PAC-J-APPL-MATH,
  volume =       "6",
  number =       "3",
  pages =        "175--187",
  year =         "2014",
  ISSN =         "1941-3963",
  MRclass =      "26E60",
  MRnumber =     "3287241",
  MRreviewer =   "Raghib M. Abu-Saris",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Applied Mathematics",
  journal-URL =  "http://www.novapublishers.com/catalog/product_info.php?products_id=6697",
}

@Article{Yang:2014:OGC,
  author =       "Lun Yang and Yue-Ying Yang and Qing Wang and Wei-Mao
                 Qian",
  title =        "The optimal geometric combination bounds for {Neuman}
                 means of harmonic, arithmetic and contra-harmonic",
  journal =      j-PAC-J-APPL-MATH,
  volume =       "6",
  number =       "4",
  pages =        "283--292",
  year =         "2014",
  ISSN =         "1941-3963",
  MRclass =      "26E60",
  MRnumber =     "3380234",
  MRreviewer =   "Yu-ming Chu",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Applied Mathematics",
  journal-URL =  "http://www.novapublishers.com/catalog/product_info.php?products_id=6697",
}

@Article{Yang:2014:SBA,
  author =       "Zhen-Hang Yang and Ying-Qing Song and Yu-Ming Chu",
  title =        "Sharp bounds for the arithmetic--geometric mean",
  journal =      j-J-INEQUAL-APPL,
  pages =        "192:1--192:13",
  year =         "2014",
  DOI =          "https://doi.org/10.1186/1029-242X-2014-192",
  ISSN =         "1029-242X",
  MRclass =      "26E60 (26D07 33E05)",
  MRnumber =     "3255894",
  MRreviewer =   "Huan Nan Shi",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Inequalities and Applications",
  journal-URL =  "http://journalofinequalitiesandapplications.springeropen.com/",
  pagecount =    "13",
}

@Article{Yang:2014:SBS,
  author =       "Zhen-Hang Yang",
  title =        "Sharp bounds for {Seiffert} mean in terms of weighted
                 power means of arithmetic mean and geometric mean",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "17",
  number =       "2",
  pages =        "499--511",
  year =         "2014",
  DOI =          "https://doi.org/10.7153/mia-17-37",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "26E60",
  MRnumber =     "3235026",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Zhao:2014:OII,
  author =       "Jianguo Zhao and Junliang Wu and Haisong Cao and
                 Wenshi Liao",
  title =        "Operator inequalities involving the arithmetic,
                 geometric, {Heinz} and {Heron} means",
  journal =      j-J-MATH-INEQUAL,
  volume =       "8",
  number =       "4",
  pages =        "747--756",
  year =         "2014",
  DOI =          "https://doi.org/10.7153/jmi-08-56",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "47A05 (26D10 26E60)",
  MRnumber =     "3277368",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Zuo:2014:UBS,
  author =       "Hongliang Zuo and Masatoshi Fujii and Jun Ichi Fujii
                 and Yuki Seo",
  title =        "Upper bound for spectra of {Jensen} operator and its
                 application to reverse arithmetic--geometric means",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "17",
  number =       "2",
  pages =        "641--648",
  year =         "2014",
  DOI =          "https://doi.org/10.7153/mia-17-47",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "47A10 (47A30)",
  MRnumber =     "3235036",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Audenaert:2015:IBA,
  author =       "Koenraad M. R. Audenaert",
  title =        "Interpolating between the arithmetic--geometric mean
                 and {Cauchy--Schwarz} matrix norm inequalities",
  journal =      j-OPER-MATRICES,
  volume =       "9",
  number =       "2",
  pages =        "475--479",
  year =         "2015",
  DOI =          "https://doi.org/10.7153/oam-09-29",
  ISSN =         "1846-3886 (print), 1848-9974 (electronic)",
  MRclass =      "15A60",
  MRnumber =     "3338577",
  MRreviewer =   "Rajendra Bhatia",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Operators and Matrices",
  journal-URL =  "http://oam.ele-math.com/",
}

@Article{Buric:2015:AEA,
  author =       "Tomislav Buri{\'c} and Neven Elezovi{\'c}",
  title =        "Asymptotic expansion of the arithmetic--geometric mean
                 and related inequalities",
  journal =      j-J-MATH-INEQUAL,
  volume =       "9",
  number =       "4",
  pages =        "1181--1190",
  year =         "2015",
  DOI =          "https://doi.org/10.7153/jmi-09-90",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "26E60 (41A60)",
  MRnumber =     "3360162",
  MRreviewer =   "Silvia Toader",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Chu:2015:OBF,
  author =       "Yu-Ming Chu and Wei-Mao Qian and Li-Min Wu and
                 Xiao-Hui Zhang",
  title =        "Optimal bounds for the first and second {Seiffert}
                 means in terms of geometric, arithmetic and
                 contraharmonic means",
  journal =      j-J-INEQUAL-APPL,
  pages =        "44:1--44:9",
  year =         "2015",
  DOI =          "https://doi.org/10.1186/s13660-015-0570-2",
  ISSN =         "1029-242X",
  MRclass =      "26E60",
  MRnumber =     "3305713",
  MRreviewer =   "Raghib M. Abu-Saris",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Inequalities and Applications",
  journal-URL =  "http://journalofinequalitiesandapplications.springeropen.com/",
}

@Article{Gao:2015:DWM,
  author =       "Peng Gao",
  title =        "On a discrete weighted mixed arithmetic--geometric
                 mean inequality",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "18",
  number =       "3",
  pages =        "941--947",
  year =         "2015",
  DOI =          "https://doi.org/10.7153/mia-18-70",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "26E60 (26D15)",
  MRnumber =     "3344739",
  MRreviewer =   "Eder Kikianty",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Leng:2015:SUB,
  author =       "Tuo Leng and Xiaolin Qin",
  title =        "The sharp upper bound for the ratio between the
                 arithmetic and the geometric mean",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "18",
  number =       "3",
  pages =        "975--980",
  year =         "2015",
  DOI =          "https://doi.org/10.7153/mia-18-73",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "26E60 (26D15)",
  MRnumber =     "3344742",
  MRreviewer =   "{\'A}d{\'a}m Besenyei",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Nelsen:2015:PWT,
  author =       "Roger B. Nelsen",
  title =        "Proof Without Words: a Trigonometric Proof of the
                 Arithmetic Mean--Geometric Mean Inequality",
  journal =      j-COLLEGE-MATH-J,
  volume =       "46",
  number =       "1",
  pages =        "42--42",
  month =        jan,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.4169/college.math.j.46.1.42",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 10:09:33 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.4169/college.math.j.46.1.42",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  onlinedate =   "27 Nov 2017",
}

@Article{Nishimura:2015:NPL,
  author =       "Ryo Nishimura",
  title =        "New properties of the lemniscate function and its
                 transformation",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "427",
  number =       "1",
  pages =        "460--468",
  year =         "2015",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/j.jmaa.2015.02.066",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X15001870",
  abstract =     "In this paper, we show several formulas for the
                 lemniscate function which include an infinite product
                 formula for the lemniscate sine. Furthermore, we show
                 the relation between the product formula and Carlson's
                 algorithm which is known as the variant of the
                 arithmetic geometric mean of Gauss.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "Hypergeometric series; Infinite products; Lemniscate
                 function; Mean iteration",
}

@Article{Osler:2015:PNR,
  author =       "Thomas J. Osler",
  title =        "A Product of Nested Radicals for the {AGM}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "122",
  number =       "9",
  pages =        "886--887",
  month =        nov,
  year =         "2015",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.122.9.886",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Feb 8 16:33:32 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib",
  URL =          "http://www.jstor.org/stable/10.4169/amer.math.monthly.122.9.886",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Pinelis:2015:EUL,
  author =       "Iosif Pinelis",
  title =        "Exact upper and lower bounds on the difference between
                 the arithmetic and geometric means",
  journal =      j-BULL-AUSTRAL-MATH-SOC,
  volume =       "92",
  number =       "1",
  pages =        "149--158",
  year =         "2015",
  CODEN =        "ALNBAB",
  DOI =          "https://doi.org/10.1017/S0004972715000350",
  ISSN =         "0004-9727 (print), 1755-1633 (electronic)",
  ISSN-L =       "0004-9727",
  MRclass =      "60E15 (26E60)",
  MRnumber =     "3366459",
  MRreviewer =   "Yuanguo Zhu",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin of the Australian Mathematical Society",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
}

@Article{Qian:2015:SBS,
  author =       "Wei-Mao Qian and Yu-Ming Chu and Xiao-Hui Zhang",
  title =        "Sharp bounds for {S{\'a}ndor} mean in terms of
                 arithmetic, geometric and harmonic means",
  journal =      j-J-INEQUAL-APPL,
  pages =        "221:1--221:13",
  year =         "2015",
  DOI =          "https://doi.org/10.1186/s13660-015-0741-1",
  ISSN =         "1029-242X",
  MRclass =      "26E60",
  MRnumber =     "3367707",
  MRreviewer =   "Raghib M. Abu-Saris",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Inequalities and Applications",
  journal-URL =  "http://journalofinequalitiesandapplications.springeropen.com/",
}

@Article{Ruan:2015:NAG,
  author =       "Jiechang Ruan",
  title =        "Notes on the arithmetic--geometric mean inequality for
                 singular values",
  journal =      j-ITAL-J-PURE-APPL-MATH,
  volume =       "35",
  pages =        "227--232",
  year =         "2015",
  ISSN =         "1126-8042 (print), 2239-0227 (electronic)",
  MRclass =      "15A42 (47A63 47B15)",
  MRnumber =     "3477563",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Italian Journal of Pure and Applied Mathematics",
  journal-URL =  "http://ijpam.uniud.it/journal/",
}

@Article{Xu:2015:RSP,
  author =       "Qian Xu",
  title =        "Research on {Schur}-$p$ power-convexity of the
                 quotient of arithmetic mean and geometric mean",
  journal =      "J. Fudan Univ. Nat. Sci.",
  volume =       "54",
  number =       "3",
  pages =        "288--295",
  year =         "2015",
  ISSN =         "0427-7104",
  MRclass =      "26E60 (26B25)",
  MRnumber =     "3410771",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Fudan University. Journal. Natural Science. Fudan
                 Xuebao. Ziran Kexue Ban",
}

@Article{Zou:2015:IAG,
  author =       "Limin Zou and Youyi Jiang",
  title =        "Improved arithmetic--geometric mean inequality and its
                 application",
  journal =      j-J-MATH-INEQUAL,
  volume =       "9",
  number =       "1",
  pages =        "107--111",
  year =         "2015",
  DOI =          "https://doi.org/10.7153/jmi-09-10",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "47A63 (26D07 26E60)",
  MRnumber =     "3333909",
  MRreviewer =   "Ali Morassaei",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Zou:2015:RAG,
  author =       "Limin Zou and Yi Huang",
  title =        "A refinement of the arithmetic--geometric mean
                 inequality",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "46",
  number =       "1",
  pages =        "158--160",
  year =         "2015",
  CODEN =        "IJMEBM",
  DOI =          "https://doi.org/10.1080/0020739X.2014.941426",
  ISSN =         "0020-739x (print), 1464-5211 (electronic)",
  ISSN-L =       "0020-739X",
  MRclass =      "26D15",
  MRnumber =     "3286728",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  journal-URL =  "http://www.tandfonline.com/loi/tmes20",
}

@Article{Zuo:2015:IRA,
  author =       "Hongliang Zuo and Nan Cheng",
  title =        "Improved reverse arithmetic--geometric means
                 inequalities for positive operators on {Hilbert}
                 space",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "18",
  number =       "1",
  pages =        "51--60",
  year =         "2015",
  DOI =          "https://doi.org/10.7153/mia-18-03",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "47A30 (47A63)",
  MRnumber =     "3277056",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Adiyasuren:2016:RAG,
  author =       "Vandanjav Adiyasuren and Tserendorj Batbold and
                 Muhammad Adil Khan",
  title =        "Refined arithmetic--geometric mean inequality and new
                 entropy upper bound",
  journal =      j-COMMUN-KOREAN-MATH-SOC,
  volume =       "31",
  number =       "1",
  pages =        "95--100",
  year =         "2016",
  DOI =          "https://doi.org/10.4134/CKMS.2016.31.1.095",
  ISSN =         "1225-1763 (print), 2234-3024 (electronic)",
  MRclass =      "94A17 (26E60)",
  MRnumber =     "3458733",
  MRreviewer =   "Flavia-Corina Mitroi-Symeonidis",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Korean Mathematical Society. Communications",
  journal-URL =  "http://ckms.kms.or.kr/",
}

@InCollection{Agarwal:2016:BGC,
  author =       "Ravi Agarwal and Hans Agarwal and Syamal Sen",
  title =        "Birth, growth and computation of pi to ten trillion
                 digits (2013)",
  crossref =     "Bailey:2016:PNG",
  pages =        "363--423",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_22",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Almkvist:2016:GLR,
  author =       "Gert Almkvist and Bruce Berndt",
  title =        "{Gauss}, {Landen}, {Ramanujan}, the
                 arithmetic--geometric mean, ellipses, $ \pi $, and the
                 {{\booktitle{Ladies Diary}}} (1988)",
  crossref =     "Bailey:2016:PNG",
  pages =        "125--150",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_8",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Bailey:2016:CDD,
  author =       "David H. Bailey",
  title =        "The computation of $ \pi $ to 29,360,000 decimal
                 digits using {Borweins}' quartically convergent
                 algorithm (1988)",
  crossref =     "Bailey:2016:PNG",
  pages =        "109--124",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_7",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Bailey:2016:CPI,
  author =       "David H. Bailey and Jonathan M. Borwein and Andrew
                 Mattingly and Glenn Wightwick",
  title =        "The computation of previously inaccessible digits of $
                 \pi $",
  crossref =     "Bailey:2016:PNG",
  pages =        "327--339",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_20",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Bailey:2016:RCV,
  author =       "David H. Bailey and Peter B. Borwein and Simon
                 Plouffe",
  title =        "On the rapid computation of various polylogarithmic
                 constants (1997)",
  crossref =     "Bailey:2016:PNG",
  pages =        "219--231",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_?",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bakherad:2016:RRG,
  author =       "Mojtaba Bakherad",
  title =        "Refinements of a reversed {AM--GM} operator
                 inequality",
  journal =      j-LIN-MULT-ALGEBRA,
  volume =       "64",
  number =       "9",
  pages =        "1687--1695",
  year =         "2016",
  CODEN =        "LNMLAZ",
  DOI =          "https://doi.org/10.1080/03081087.2015.1114984",
  ISSN =         "0308-1087 (print), 1563-5139 (electronic)",
  ISSN-L =       "0308-1087",
  bibdate =      "Tue Sep 20 15:15:01 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/linmultalgebra.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Multilinear Algebra",
  journal-URL =  "http://www.tandfonline.com/loi/glma20",
  onlinedate =   "01 Dec 2015",
}

@InCollection{Borwein:2016:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The arithmetic--geometric mean and fast computation of
                 elementary functions (1984)",
  crossref =     "Bailey:2016:PNG",
  pages =        "79--96",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_4",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-319-32377-0_4",
  acknowledgement = ack-nhfb,
}

@InCollection{Borwein:2016:RME,
  author =       "Jonathan M. Borwein and Peter B. Borwein and David H.
                 Bailey",
  title =        "{Ramanujan}, modular equations, and approximations to
                 pi or how to compute one billion digits of pi (1989)",
  crossref =     "Bailey:2016:PNG",
  pages =        "175--195",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_?",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Brent:2016:FMP,
  author =       "Richard P. Brent",
  title =        "Fast multiple-precision evaluation of elementary
                 functions (1976)",
  crossref =     "Bailey:2016:PNG",
  pages =        "9--20",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_2",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Buric:2016:AAI,
  author =       "Tomislav Buri{\'c}",
  title =        "Asymptotic analysis of the iterative power means",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "433",
  number =       "1",
  pages =        "701--705",
  year =         "2016",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/j.jmaa.2015.08.020",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X15007477",
  abstract =     "We investigate the asymptotic expansion of the
                 compound mean obtained by the iterative process of two
                 power means. We present the stationary and convergence
                 properties of the coefficients in the expansions.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "Arithmetic--geometric mean; Asymptotic expansion;
                 Compound mean; Power mean",
}

@Article{Cardoso:2016:MAG,
  author =       "Jo{\~a}o R. Cardoso and Rui Ralha",
  title =        "Matrix Arithmetic--Geometric Mean and the Computation
                 of the Logarithm",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "37",
  number =       "2",
  pages =        "719--743",
  month =        "????",
  year =         "2016",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/140998226",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F60 (33E05 65F30)",
  MRnumber =     "3507553",
  MRreviewer =   "Volker Karl Richard Grimm",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/2;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2016",
}

@InCollection{Cox:2016:AGM,
  author =       "David A. Cox",
  title =        "The arithmetic--geometric mean of {Gauss} (1984)",
  crossref =     "Bailey:2016:PNG",
  pages =        "21--78",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_3",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Fujii:2016:RDM,
  author =       "Jun Ichi Fujii and Masatoshi Fujii and Yuki Seo and
                 Hongliang Zuo",
  title =        "Recent developments of matrix versions of the
                 arithmetic--geometric mean inequality",
  journal =      j-ANN-FUNCT-ANAL,
  volume =       "7",
  number =       "1",
  pages =        "102--117",
  year =         "2016",
  DOI =          "https://doi.org/10.1215/20088752-3429400",
  ISSN =         "2008-8752",
  MRclass =      "47A63 (15A18 15A42 47-02 47A30)",
  MRnumber =     "3449343",
  MRreviewer =   "Rajendra Bhatia",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Functional Analysis",
  journal-URL =  "http://projecteuclid.org/afa",
}

@Article{Guo:2016:SBN,
  author =       "Zhi-Jun Guo and Yan Zhang and Yu-Ming Chu and
                 Ying-Qing Song",
  title =        "Sharp bounds for {Neuman} means in terms of geometric,
                 arithmetic and quadratic means",
  journal =      j-J-MATH-INEQUAL,
  volume =       "10",
  number =       "2",
  pages =        "301--312",
  year =         "2016",
  DOI =          "https://doi.org/10.7153/jmi-10-25",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "26E60",
  MRnumber =     "3455365",
  MRreviewer =   "Wei-Dong Jiang",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Hirzallah:2016:SVC,
  author =       "Omar Hirzallah",
  title =        "Singular values of convex functions of operators and
                 the arithmetic--geometric mean inequality",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "433",
  number =       "2",
  pages =        "935--947",
  year =         "2016",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/j.jmaa.2015.08.036",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "47A63",
  MRnumber =     "3398744",
  MRreviewer =   "Eizaburo Kamei",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X15007635",
  abstract =     "We prove singular value inequalities for convex
                 functions of products and sums of operators that
                 generalize the arithmetic--geometric mean inequality
                 for operators. Among other results, we prove that if $
                 A_i, B_i, X_i, Y_i $, $ i = 1, \ldots, n $ are
                 operators on a complex separable Hilbert space such
                 that $ | X_i | 2 + | Y_i | 2 2 n \leq I $, $ i = 1,
                 \ldots, n $ and if $f$ is a nonnegative increasing
                 convex function on $ [0, \infty)$ satisfying $ f (0) =
                 0$, then $ s_j (f (| \sum_{i = 1}^n A_i X_i Y_i^\star
                 B_i^\star |)) \leq (1 / 2) s_j (\oplus_{k = 1}^n
                 (X_k^\star (\sum_{i = 1}^n f(| A_i^\star A_k |)) X_k +
                 Y_k^\star (\sum_{i = 1}^n f(| B_i^\star B_k |)) Y_k))$
                 for $ j = 1, 2, \ldots $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "Compact operator; Convex function; Inequality;
                 Positive operator; Singular value",
}

@Article{Hoffmann:2016:WGI,
  author =       "Heiko Hoffmann",
  title =        "Weighted {AM--GM} Inequality via Elementary
                 Multivariable Calculus",
  journal =      j-COLLEGE-MATH-J,
  volume =       "47",
  number =       "1",
  pages =        "56--58",
  month =        jan,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.4169/college.math.j.47.1.56",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 10:09:43 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.4169/college.math.j.47.1.56",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  onlinedate =   "27 Nov 2017",
}

@Article{Israel:2016:AGM,
  author =       "Arie Israel and Felix Krahmer and Rachel Ward",
  title =        "An arithmetic--geometric mean inequality for products
                 of three matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "488",
  number =       "??",
  pages =        "1--12",
  day =          "1",
  month =        jan,
  year =         "2016",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2015.09.013",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A45",
  MRnumber =     "3419770",
  MRreviewer =   "Tanvi Jain",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2015.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379515005285",
  abstract =     "Consider the following noncommutative
                 arithmetic--geometric mean inequality: Given
                 positive-semidefinite matrices $ A_1, \ldots, A_n $,
                 the following holds for each integer $ m \leq n $: $ (1
                 / n^m) \sum_{j_1, j_2, \ldots, j_m = 1}^n ||| A_{j_1}
                 A_{j_2} \ldots A_{j_m} ||| \geq ((n - m)! / n!)
                 \sum_{j_1, j_2, \ldots, j_m} = 1 ({\rm all distinct})^n
                 ||| A_{j_1} A_{j_2} \ldots A_{j_m} ||| $, where $ |||
                 \cdot ||| $ denotes a unitarily invariant norm,
                 including the operator norm and Schatten $p$-norms as
                 special cases. While this inequality in full generality
                 remains a conjecture, we prove that the inequality
                 holds for products of up to three matrices, $ m \leq
                 3$. The proofs for $ m = 1, 2$ are straightforward; to
                 derive the proof for $ m = 3$, we appeal to a variant
                 of the classic Araki--Lieb--Thirring inequality for
                 permutations of matrix products.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
  keywords =     "Arithmetic--geometric mean inequality; Linear algebra;
                 Norm inequalities",
}

@InCollection{Kanada:2016:VMP,
  author =       "Yasumasa Kanada",
  title =        "Vectorization of multiple-precision arithmetic program
                 and 201,326,000 decimal digits of pi calculation
                 (1988)",
  crossref =     "Bailey:2016:PNG",
  pages =        "151--164",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_9",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Newman:2016:SVF,
  author =       "D. J. Newman",
  title =        "A simplified version of the fast algorithms of {Brent}
                 and {Salamin} (1985)",
  crossref =     "Bailey:2016:PNG",
  pages =        "97--102",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_5",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Salamin:2016:CUA,
  author =       "Eugene Salamin",
  title =        "Computation of $ \pi $ using arithmetic--geometric
                 mean (1976)",
  crossref =     "Bailey:2016:PNG",
  pages =        "1--8",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_1",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sheikhhosseini:2016:NRV,
  author =       "Alemeh Sheikhhosseini",
  title =        "A numerical radius version of the
                 arithmetic--geometric mean of operators",
  journal =      "Filomat",
  volume =       "30",
  number =       "8",
  pages =        "2139--2145",
  year =         "2016",
  DOI =          "https://doi.org/10.2298/FIL1608139S",
  ISSN =         "0354-5180",
  MRclass =      "47A30 (47A12)",
  MRnumber =     "3583150",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Univerzitet u Ni{\v{s}}u. Prirodno-Matemati{\v{c}}ki
                 Fakultet. Filomat",
}

@Misc{Singh:2016:PAL,
  author =       "Paramanand Singh",
  title =        "$ \pi $ ({PI}) and the {AGM}: {Legendre}'s Identity",
  howpublished = "Web site",
  year =         "2016",
  bibdate =      "Tue Mar 14 10:19:25 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "https://paramanands.blogspot.com/2009/08/pi-and-the-agm-legendres-identity.html",
  acknowledgement = ack-nhfb,
}

@Article{Wang:2016:OBG,
  author =       "Hua Wang and Wei-Mao Qian and Yu-Ming Chu",
  title =        "Optimal bounds for {Gaussian} arithmetic--geometric
                 mean with applications to complete elliptic integral",
  journal =      j-FUNCT-SPACES,
  pages =        "3698463:1--3698463:6",
  year =         "2016",
  DOI =          "https://doi.org/10.1155/2016/3698463",
  ISSN =         "2314-8896",
  MRclass =      "26E60 (33E05)",
  MRnumber =     "3531324",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Function Spaces",
  journal-URL =  "https://www.hindawi.com/journals/jfs/",
}

@Article{Zou:2016:NIB,
  author =       "Limin Zou and Youyi Jiang",
  title =        "A note on interpolation between the
                 arithmetic--geometric mean and {Cauchy--Schwarz} matrix
                 norm inequalities",
  journal =      j-J-MATH-INEQUAL,
  volume =       "10",
  number =       "4",
  pages =        "1119--1122",
  year =         "2016",
  DOI =          "https://doi.org/10.7153/jmi-10-88",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "15A60 (47A63)",
  MRnumber =     "3581159",
  MRreviewer =   "Mitsuru Uchiyama",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@TechReport{Brent:2017:JBP,
  author =       "Richard P. Brent",
  title =        "{Jonathan Borwein}, Pi and the {AGM}",
  type =         "Talk slides",
  institution =  "Australian National University and CARMA, University
                 of Newcastle",
  address =      "Canberra, ACT and Newcastle, NSW, Australia",
  pages =        "76",
  day =          "26",
  month =        sep,
  year =         "2017",
  bibdate =      "Fri Sep 04 17:08:54 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://carma.newcastle.edu.au/meetings/jbcc/abstracts/pdf/JBCC-Richard_Brent.pdf",
  abstract =     "We consider some of Jon Borwein s contributions to the
                 high-precision computation of $ \pi $ and the
                 elementary functions, with particular reference to the
                 fascinating book \booktitle{Pi and the AGM}(Wiley,
                 1987) by Jon and his brother Peter Borwein. Here
                 ``AGM'' is the arithmetic-geometric mean, first studied
                 by Euler, Gauss and Legendre. Because the AGM has
                 second-order convergence, it can be combined with fast
                 multiplication algorithms to give fast algorithms for
                 the $n$-bit computation of $ \pi $, and more generally
                 the elementary functions. These algorithms run in
                 ``almost linear' time $ O(M(n) \log n)$, where $ M(n)$
                 is the time for $n$-bit multiplication. The talk will
                 survey some of the results and algorithms, from the
                 time of Archimedes to the present day, that were of
                 interest to Jon. In several cases they were discovered
                 or improved by him",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}

@Article{Buric:2017:CAA,
  author =       "Tomislav Buri{\'c} and Neven Elezovi{\'c}",
  title =        "Computation and analysis of the asymptotic expansions
                 of the compound means",
  journal =      j-APPL-MATH-COMP,
  volume =       "303",
  number =       "??",
  pages =        "48--54",
  year =         "2017",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2017.01.025",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300317300334",
  abstract =     "We derive algorithms for computing asymptotic
                 expansion of the composite mean of two arbitrary means
                 M and N. Then we analyse asymptotic behaviour of the
                 compound mean $ M \otimes N $. Examples and application
                 to some classical means are also presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "Arithmetic--geometric mean; Asymptotic expansion;
                 Compound mean; Power mean",
}

@Article{Chang:2017:AGM,
  author =       "Chun-Tao Chang and Liang-Yuh Ouyang",
  title =        "An arithmetic--geometric mean inequality approach for
                 determining the optimal production lot size with
                 backlogging and imperfect rework process",
  journal =      "J. Appl. Anal. Comput.",
  volume =       "7",
  number =       "1",
  pages =        "224--235",
  year =         "2017",
  ISSN =         "2156-907X",
  MRclass =      "90B05",
  MRnumber =     "3528209",
  MRreviewer =   "Jian-Teng Xu",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of Applied Analysis and Computation",
}

@Article{Choi:2017:IRA,
  author =       "D. Choi and M. Sababheh",
  title =        "Inequalities related to the arithmetic, geometric and
                 harmonic means",
  journal =      j-J-MATH-INEQUAL,
  volume =       "11",
  number =       "1",
  pages =        "1--16",
  year =         "2017",
  DOI =          "https://doi.org/10.7153/jmi-11-01",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "26E60 (47A63)",
  MRnumber =     "3601921",
  MRreviewer =   "Wei-Dong Jiang",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Ding:2017:OBA,
  author =       "Qing Ding and Tiehong Zhao",
  title =        "Optimal bounds for arithmetic--geometric and {Toader}
                 means in terms of generalized logarithmic mean",
  journal =      j-J-INEQUAL-APPL,
  pages =        "102:1--102:12",
  year =         "2017",
  DOI =          "https://doi.org/10.1186/s13660-017-1365-4",
  ISSN =         "1029-242X",
  MRclass =      "26E60",
  MRnumber =     "3647198",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Inequalities and Applications",
  journal-URL =  "http://journalofinequalitiesandapplications.springeropen.com/",
}

@Article{Griffiths:2017:AGM,
  author =       "Martin Griffiths and Des MacHale",
  title =        "On arithmetic--geometric-mean polynomials",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "48",
  number =       "1",
  pages =        "111--117",
  year =         "2017",
  CODEN =        "IJMEBM",
  DOI =          "https://doi.org/10.1080/0020739X.2016.1172740",
  ISSN =         "0020-739x (print), 1464-5211 (electronic)",
  ISSN-L =       "0020-739X",
  MRclass =      "26D05 (26E60)",
  MRnumber =     "3580860",
  MRreviewer =   "Zhen-Hang Yang",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  journal-URL =  "http://www.tandfonline.com/loi/tmes20",
}

@Article{Iannazzo:2017:RBB,
  author =       "Bruno Iannazzo and Margherita Porcelli",
  title =        "The {Riemannian Barzilai--Borwein} method with
                 nonmonotone line search and the matrix geometric mean
                 computation",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "38",
  number =       "1",
  pages =        "495--517",
  month =        apr,
  year =         "2017",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/drx015",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  bibdate =      "Fri Feb 9 09:25:58 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}

@Article{Rodin:2017:VIA,
  author =       "Burt Rodin",
  title =        "Variance and the inequality of arithmetic and
                 geometric means",
  journal =      j-ROCKY-MOUNTAIN-J-MATH,
  volume =       "47",
  number =       "2",
  pages =        "637--648",
  year =         "2017",
  CODEN =        "RMJMAE",
  DOI =          "https://doi.org/10.1216/RMJ-2017-47-2-637",
  ISSN =         "0035-7596 (print), 1945-3795 (electronic)",
  ISSN-L =       "0035-7596",
  MRclass =      "26D07 (26E60)",
  MRnumber =     "3635378",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Rocky Mountain Journal of Mathematics",
  journal-URL =  "http://projecteuclid.org/euclid.rmjm",
}

@Article{Sawhney:2017:TPG,
  author =       "Mehtaab S. Sawhney",
  title =        "A Telescoping Proof of the {AM--GM} Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "124",
  number =       "4",
  pages =        "356--356",
  month =        apr,
  year =         "2017",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.124.4.356",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Oct 30 07:18:01 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib",
  URL =          "http://www.jstor.org/stable/10.4169/amer.math.monthly.124.4.356",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Sheikhhosseini:2017:AGM,
  author =       "Alemeh Sheikhhosseini",
  title =        "An arithmetic--geometric mean inequality related to
                 numerical radius of matrices",
  journal =      "Konuralp J. Math.",
  volume =       "5",
  number =       "1",
  pages =        "85--91",
  year =         "2017",
  ISSN =         "2147-625X",
  MRclass =      "15A60 (26E60)",
  MRnumber =     "3637699",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Konuralp Journal of Mathematics",
}

@Article{Wu:2017:NYA,
  author =       "Yanqiu Wu",
  title =        "Note on {Young} and arithmetic--geometric mean
                 inequalities for matrices",
  journal =      j-ITAL-J-PURE-APPL-MATH,
  volume =       "37",
  pages =        "347--350",
  year =         "2017",
  ISSN =         "1126-8042 (print), 2239-0227 (electronic)",
  MRclass =      "15A42",
  MRnumber =     "3622936",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Italian Journal of Pure and Applied Mathematics",
  journal-URL =  "http://ijpam.uniud.it/journal/",
}

@Article{Xue:2017:RWA,
  author =       "Jianming Xue",
  title =        "On reverse weighted arithmetic--geometric mean
                 inequalities for two positive operators",
  journal =      j-ITAL-J-PURE-APPL-MATH,
  volume =       "37",
  pages =        "113--116",
  year =         "2017",
  ISSN =         "1126-8042 (print), 2239-0227 (electronic)",
  MRclass =      "47A63 (47A30)",
  MRnumber =     "3622918",
  bibdate =      "Tue Aug 15 09:24:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Italian Journal of Pure and Applied Mathematics",
  journal-URL =  "http://ijpam.uniud.it/journal/",
}

@Article{Zou:2017:AGM,
  author =       "Limin Zou",
  title =        "An arithmetic--geometric mean inequality for singular
                 values and its applications",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "528",
  number =       "??",
  pages =        "25--32",
  day =          "1",
  month =        sep,
  year =         "2017",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2016.01.016",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A42 (47A63)",
  MRnumber =     "3652834",
  bibdate =      "Tue Aug 15 10:10:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2015.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379516000185",
  abstract =     "In this short note, we give a new equivalent form of
                 the arithmetic--geometric mean inequality for singular
                 values. As applications of our result, we give a new
                 proof of an inequality due to Bhatia and Davis (1993)
                 [4] and we obtain a singular value inequality for
                 matrix means, which is similar to one proved by Drury
                 (2012) [9]. Finally, we present a log-majorization
                 inequality for singular values.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Matrix means; Singular values; Unitarily invariant
                 norms",
}

@Article{Bertot:2018:DDP,
  author =       "Yves Bertot and Laurence Rideau and Laurent
                 Th{\'e}ry",
  title =        "Distant Decimals of $ \pi $: Formal Proofs of Some
                 Algorithms Computing Them and Guarantees of Exact
                 Computation",
  journal =      j-J-AUTOM-REASON,
  volume =       "61",
  number =       "1--4",
  pages =        "33--71",
  month =        jun,
  year =         "2018",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1007/s10817-017-9444-2",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Sat Aug 4 07:51:41 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  URL =          "http://link.springer.com/article/10.1007/s10817-017-9444-2",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
  keywords =     "Arithmetic geometric means; Bailey, Borwein, and
                 Plouffe formula; BBP; Coq proof assistant; Formal
                 proofs in real analysis; PI",
}

@Article{Gencev:2018:PIB,
  author =       "Marian Gencev",
  title =        "On a Proof of the Inequality Between the Arithmetic
                 and Geometric Means",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "125",
  number =       "7",
  pages =        "650--652",
  year =         "2018",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2018.1470422",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 17:59:05 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "03 Aug 2018",
}

@Article{Jameson:2018:RNA,
  author =       "G. J. O. Jameson",
  title =        "102.45 {Revisiting} a note on arithmetic and geometric
                 means",
  journal =      j-MATH-GAZ,
  volume =       "102",
  number =       "555",
  pages =        "513",
  month =        nov,
  year =         "2018",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.1017/mag.2018.125",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Thu Feb 14 07:32:40 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
  URL =          "https://www.cambridge.org/core/journals/mathematical-gazette/article/10245-revisiting-a-note-on-arithmetic-and-geometric-means/7D7E5F6E956573FB16FCB8998A9E3193",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayIssue?jid=MAG;
                 http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  onlinedate =   "17 October 2018",
}

@Article{Zou:2019:UAG,
  author =       "Limin Zou",
  title =        "Unification of the arithmetic-geometric mean and
                 {H{\"o}lder} inequalities for unitarily invariant
                 norms",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "562",
  number =       "??",
  pages =        "154--162",
  day =          "1",
  month =        feb,
  year =         "2019",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2018.09.030",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Thu Dec 27 15:29:01 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2015.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379518304713",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@InProceedings{Brent:2020:BBP,
  author =       "Richard P. Brent",
  title =        "The {Borwein} Brothers, Pi and the {AGM}",
  crossref =     "Bailey:2020:AVC",
  pages =        "323--347",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_21",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}

@Article{Graham:2020:EPA,
  author =       "Cole Graham and Tadashi Tokieda",
  title =        "An Entropy Proof of the Arithmetic Mean-Geometric Mean
                 Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "127",
  number =       "6",
  pages =        "545--546",
  year =         "2020",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2020.1738827",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:46 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "21 May 2020",
}

@Article{Hajja:2020:MPG,
  author =       "Mowaffaq Hajja",
  title =        "104.17 {More} proofs of the {AM--GM} inequality",
  journal =      j-MATH-GAZ,
  volume =       "104",
  number =       "560",
  pages =        "318--326",
  month =        jul,
  year =         "2020",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.1017/mag.2020.59",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Mon Aug 10 09:47:34 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2020.bib",
  URL =          "https://www.cambridge.org/core/journals/mathematical-gazette/article/10417-more-proofs-of-the-amgm-inequality/089FD8AFA839D001F8C8BDC97E438896",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayIssue?jid=MAG;
                 http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  onlinedate =   "18 June 2020",
}

@Article{Mahmoudi:2020:GIG,
  author =       "M. G. Mahmoudi",
  title =        "The {AM--GM} Inequality via Gradient",
  journal =      j-COLLEGE-MATH-J,
  volume =       "51",
  number =       "2",
  pages =        "141--143",
  year =         "2020",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.2020.1697605",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Mon Mar 9 11:58:57 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.tandfonline.com/doi/full/10.1080/07468342.2020.1697605",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  onlinedate =   "25 Feb 2020",
}

@Article{Plaza:2020:HLA,
  author =       "Angel Plaza",
  title =        "Harmonic, Logarithmic, and Arithmetic Means and
                 Corollaries",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "127",
  number =       "5",
  pages =        "427--427",
  year =         "2020",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2020.1726705",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:45 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "23 Apr 2020",
}

@Article{Moustrou:2022:SRG,
  author =       "Philippe Moustrou and Helen Naumann and Cordian Riener
                 and Thorsten Theobald and Hugues Verdure",
  title =        "Symmetry Reduction in {AM/GM}-Based Optimization",
  journal =      j-SIAM-J-OPT,
  volume =       "32",
  number =       "2",
  pages =        "765--785",
  month =        "????",
  year =         "2022",
  CODEN =        "SJOPE8",
  DOI =          "https://doi.org/10.1137/21M1405691",
  ISSN =         "1052-6234 (print), 1095-7189 (electronic)",
  ISSN-L =       "1052-6234",
  bibdate =      "Tue Oct 17 12:21:37 MDT 2023",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/32/2;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjopt.bib",
  URL =          "https://epubs.siam.org/doi/10.1137/21M1405691",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Optimization",
  journal-URL =  "http://epubs.siam.org/siopt",
}

@Article{Plaza:2022:FBP,
  author =       "{\'A}ngel Plaza",
  title =        "106.07 {A} function-based proof of the harmonic mean
                 --- geometric mean --- arithmetic mean inequalities",
  journal =      j-MATH-GAZ,
  volume =       "106",
  number =       "565",
  pages =        "130--131",
  month =        mar,
  year =         "2022",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.1017/mag.2022.22",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Mon Jul 18 08:23:47 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2020.bib",
  URL =          "https://www.cambridge.org/core/journals/mathematical-gazette/article/10607-a-functionbased-proof-of-the-harmonic-mean-geometric-mean-arithmetic-mean-inequalities/61AA72E9B6B3A99B4A12F6C768665CFB",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayIssue?jid=MAG;
                 http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  onlinedate =   "24 February 2022",
}

@Article{Griffin:2023:AJS,
  author =       "Michael J. Griffin and Ken Ono and Neelam Saikia and
                 Wei-Lun Tsai",
  title =        "{AGM} and Jellyfish Swarms of Elliptic Curves",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "130",
  number =       "4",
  pages =        "355--369",
  year =         "2023",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2022.2160157",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Fri Aug 25 08:24:36 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "16 Feb 2023",
}

@Article{Mestrovic:2023:NIP,
  author =       "Romeo Mestrovi{\'c}",
  title =        "107.32 {A} new inductive proof of the {AM--GM}
                 inequality",
  journal =      j-MATH-GAZ,
  volume =       "107",
  number =       "570",
  pages =        "497--499",
  month =        nov,
  year =         "2023",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.1017/mag.2023.104",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Mon May 20 10:47:38 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2020.bib",
  URL =          "https://www.cambridge.org/core/journals/mathematical-gazette/article/10732-a-new-inductive-proof-of-the-am-gm-inequality/05ABEFD2218BF948BCC57F1BBDB40BF6",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayIssue?jid=MAG;
                 http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  onlinedate =   "11 October 2023",
}

@Article{Farhadian:2024:GMA,
  author =       "Reza Farhadian and Vadim Ponomarenko",
  title =        "108.29 A geometric mean--arithmetic mean ratio limit",
  journal =      j-MATH-GAZ,
  volume =       "108",
  number =       "572",
  pages =        "334--335",
  month =        jul,
  year =         "2024",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.1017/mag.2024.104",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Thu Oct 10 07:23:07 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2020.bib",
  URL =          "https://www.cambridge.org/core/journals/mathematical-gazette/article/10829-a-geometric-meanarithmetic-mean-ratio-limit/64C62A926CC14548D17A82B2E7416FCE",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayIssue?jid=MAG;
                 http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  onlinedate =   "July 2024",
}

%%% ====================================================================
%%% Cross-referenced entries must come last:

@Proceedings{Traub:1976:ACC,
  editor =       "J. F. (Joseph Frederick) Traub",
  booktitle =    "{Analytic computational complexity: Proceedings of the
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                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  title =        "{Analytic computational complexity: Proceedings of the
                 Symposium on Analytic Computational Complexity, held by
                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "ix + 239",
  year =         "1976",
  ISBN =         "0-12-697560-4",
  ISBN-13 =      "978-0-12-697560-4",
  LCCN =         "QA297 .S915 1975",
  bibdate =      "Sun Dec 30 18:48:22 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  meetingname =  "Symposium on Analytic Computational Complexity,
                 Carnegie-Mellon University, 1975.",
  remark =       "",
  subject =      "Numerical analysis; Data processing; Congresses;
                 Computational complexity",
}

@Proceedings{Martin:1988:SPN,
  editor =       "Joanne L. Martin and Stephen F. Lundstrom",
  booktitle =    "Supercomputing '88: proceedings, November 14--18,
                 1988, Orlando, Florida",
  title =        "Supercomputing '88: proceedings, November 14--18,
                 1988, Orlando, Florida",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "viii + 263",
  year =         "1988",
  ISBN =         "0-8186-0882-X (v. 1; paper), 0-8186-8882-3 (v. 1;
                 case), 0-8186-4882-1 (v. 1: microfiche) 0-8186-8923-4
                 (v. 2), 0-8186-5923-X (v. 2: microfiche), 0-8186-8923-4
                 (v. 2: case)",
  ISBN-13 =      "978-0-8186-0882-7 (v. 1; paper), 978-0-8186-8882-9 (v.
                 1; case), 978-0-8186-4882-3 (v. 1: microfiche)
                 978-0-8186-8923-9 (v. 2), 978-0-8186-5923-2 (v. 2:
                 microfiche), 978-0-8186-8923-9 (v. 2: case)",
  LCCN =         "QA76.5 .S894 1988",
  bibdate =      "Fri Aug 30 08:01:51 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  note =         "Two volumes. IEEE catalog number 88CH2617-9. IEEE
                 Computer Society Order Number 882.",
  acknowledgement = ack-nhfb,
  classification = "C5440 (Multiprocessor systems and techniques); C7300
                 (Natural sciences)",
  keywords =     "biology computing; chemistry; computational biology;
                 computational fluid dynamics; computational
                 mathematics; computational physics; flow simulation;
                 global change; mathematics computing; parallel
                 processing; physics computing; structural analysis;
                 structural engineering computing; supercomputers ---
                 congresses",
}

@Proceedings{Adams:1993:SCA,
  editor =       "E. Adams and U. Kulisch",
  booktitle =    "Scientific computing with automatic result
                 verification",
  title =        "Scientific computing with automatic result
                 verification",
  volume =       "189",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "x + 612",
  year =         "1993",
  ISBN =         "0-12-044210-8",
  ISBN-13 =      "978-0-12-044210-2",
  LCCN =         "QA76.S368 1993",
  bibdate =      "Mon Dec 18 10:27:38 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "Mathematics in science and engineering",
  acknowledgement = ack-nhfb,
}

@Proceedings{Cohen:1995:AAA,
  editor =       "G. (G{\'e}rard) Cohen and Marc Giusti and Teo Mora",
  booktitle =    "{Applied algebra, algebraic algorithms, and
                 error-correcting codes: 11th international symposium,
                 AAECC-11, Paris, France, July 1995: proceedings}",
  title =        "{Applied algebra, algebraic algorithms, and
                 error-correcting codes: 11th international symposium,
                 AAECC-11, Paris, France, July 1995: proceedings}",
  volume =       "948",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 484",
  year =         "1995",
  ISBN =         "3-540-60114-7 (softcover)",
  ISBN-13 =      "978-3-540-60114-2 (softcover)",
  LCCN =         "QA268 .A35 1995",
  bibdate =      "Tue Mar 14 15:37:05 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Lecture notes in computer science",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0815/95021560-d.html",
  acknowledgement = ack-nhfb,
  meetingname =  "AAECC-11 (1995: Paris, France)",
  subject =      "Error-correcting codes (Information theory);
                 Congresses; Algebra; Data processing; Algorithms",
}

@Proceedings{Alefeld:1996:SCV,
  editor =       "G{\"o}tz Alefeld and Andreas Frommer and Bruno Lang",
  booktitle =    "Scientific computing and validated numerics:
                 proceedings of the International Symposium on
                 Scientific Computing, Computer Arithmetic and Validated
                 Numerics SCAN-95 held in Wuppertal, Germany, September
                 26--29, 1995",
  title =        "Scientific computing and validated numerics:
                 proceedings of the International Symposium on
                 Scientific Computing, Computer Arithmetic and Validated
                 Numerics {SCAN}-95 held in Wuppertal, Germany,
                 September 26--29, 1995",
  volume =       "90",
  publisher =    "Akademie Verlag",
  address =      "Berlin, Germany",
  pages =        "340",
  year =         "1996",
  ISBN =         "3-05-501737-4",
  ISBN-13 =      "978-3-05-501737-7",
  ISSN =         "0138-3019",
  LCCN =         "QA76.95 .I575 1995",
  bibdate =      "Fri Mar 27 09:56:17 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Mathematical Research",
  acknowledgement = ack-nhfb,
}

@Proceedings{Broy:1996:DPD,
  editor =       "M. Broy",
  booktitle =    "{Deductive program design: Proceedings of the NATO
                 Advanced Study Institute on Deductive Program Design,
                 held in Marktoberdorf, Germany, July 26--August 7,
                 1994}",
  title =        "{Deductive program design: Proceedings of the NATO
                 Advanced Study Institute on Deductive Program Design,
                 held in Marktoberdorf, Germany, July 26--August 7,
                 1994}",
  volume =       "152",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 467",
  year =         "1996",
  ISBN =         "3-540-60947-4 (hardcover)",
  ISBN-13 =      "978-3-540-60947-6 (hardcover)",
  LCCN =         "QA76.9.D5 D38 1996",
  bibdate =      "Tue Mar 17 10:33:47 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "NATO ASI series. Series F, Computer and systems
                 sciences",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0812/96010788-d.html",
  acknowledgement = ack-nhfb,
  subject =      "Electronic data processing; Distributed processing;
                 Congresses; System design; Logic, Symbolic and
                 mathematical",
}

@Book{Zhang:1996:AMI,
  editor =       "H. (Hantao) Zhang",
  booktitle =    "Automated Mathematical Induction",
  title =        "Automated Mathematical Induction",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "224",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/978-94-009-1675-3",
  ISBN =         "94-010-7250-7 (print), 94-009-1675-2 (e-book)",
  ISBN-13 =      "978-94-010-7250-2 (print), 978-94-009-1675-3
                 (e-book)",
  LCCN =         "Q334-342",
  bibdate =      "Tue Mar 14 12:17:31 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://public.eblib.com/choice/publicfullrecord.aspx?p=3102529",
  abstract =     "Two decades ago, Boyer and Moore built one of the
                 first automated theorem provers that was capable of
                 proofs by mathematical induction. Today, the
                 Boyer--Moore theorem prover remains the most successful
                 in the field. For a long time, the research on
                 automated mathematical induction was confined to very
                 few people. In recent years, as more people realize the
                 importance of automated inductive reasoning to the use
                 of formal methods of software and hardware development,
                 more automated inductive proof systems have been
                 built.\par

                 Three years ago, the interested researchers in the
                 field formed two consortia on automated inductive
                 reasoning --- the MInd consortium in Europe and the
                 IndUS consortium in the United States. The two
                 consortia organized three joint workshops in
                 1992--1995. There will be another one in 1996.
                 Following the suggestions of Alan Bundy and Deepak
                 Kapur, this book documents advances in the
                 understanding of the field and in the power of the
                 theorem provers that can be built.\par

                 In the first of six papers, the reader is provided with
                 a tutorial study of the Boyer--Moore theorem prover.
                 The other five papers present novel ideas that could be
                 used to build theorem provers more powerful than the
                 Boyer-Moore prover.",
  acknowledgement = ack-nhfb,
  subject =      "Computer science; Logic; Artificial intelligence;
                 Logic, Symbolic and mathematical; Artificial
                 intelligence; Computer science; Logic; Logic, Symbolic
                 and mathematical",
  tableofcontents = "Induction Using Term Orders \\
                 New Uses of Linear Arithmetic in Automated Theorem
                 Proving by Induction \\
                 Productive Use of Failure in Inductive Proof \\
                 Middle-Out Reasoning for Synthesis and Induction \\
                 A Calculus for and Termination of Rippling \\
                 Interaction with the Boyer Moore Theorem Prover: A
                 Tutorial Study Using the Arithmetic--Geometric Mean
                 Theorem",
}

@Book{Berggren:1997:PSB,
  editor =       "Lennart Berggren and Jonathan M. Borwein and Peter B.
                 Borwein",
  booktitle =    "Pi, a source book",
  title =        "Pi, a source book",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xix + 716",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4",
  ISBN =         "0-387-94924-0, 1-4757-2736-4 (e-book), 1-4757-2738-0
                 (print), 3-540-94924-0",
  ISBN-13 =      "978-0-387-94924-6, 978-1-4757-2736-4 (e-book),
                 978-1-4757-2738-8 (print), 978-3-540-94924-4",
  LCCN =         "QA484 .P5 1997",
  bibdate =      "Fri Sep 2 17:41:50 MDT 2022",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib;
                 z3950.loc.gov:7090/Voyager",
  abstract =     "The aim of this book is to provide a complete history
                 of pi from the dawn of mathematical time to the
                 present. The story of pi reflects the most seminal, the
                 most serious and sometimes the silliest aspects of
                 mathematics, and a surprising amount of the most
                 important mathematics and mathematicians have
                 contributed to its unfolding. Pi is one of the few
                 concepts in mathematics whose mention evokes a response
                 of recognition and interest in those not concerned
                 professionally with the subject. Yet, despite this, no
                 source book on pi has been published. One of the
                 beauties of the literature on pi is that it allows for
                 the inclusion of very modern, yet still accessible,
                 mathematics. Mathematicians and historians of
                 mathematics will find this book indispensable. Teachers
                 at every level from the seventh grade onward will find
                 here ample resources for anything from special topic
                 courses to individual talks and special student
                 projects. The literature on pi included in this source
                 book falls into three classes: first a selection of the
                 mathematical literature of four millennia, second a
                 variety of historical studies or writings on the
                 cultural meaning and significance of the number, and
                 third, a number of treatments on pi that are fanciful,
                 satirical and/or whimsical.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Pi; Pi (Le nombre); Pi.; Pi (le nombre)",
  tableofcontents = "Preface / v \\
                 \\
                 Acknowledgments / ix \\
                 \\
                 Introduction / xvii \\
                 \\
                 1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$
                 1650 B.C.) / A problem dealing with the area of a round
                 field of given diameter / 1 \\
                 \\
                 2. Engels. Quadrature of the Circle in Ancient Egypt
                 (1977) / A conjectural explanation of how the
                 mathematicians of ancient Egypt approximated the area
                 of a circle / 3 \\
                 \\
                 3. Archimedes. Measurement of a Circle ($\approx$ 250
                 BC) / The seminal work in which Archimedes presents the
                 first true algorithm for $\pi$ / 7 \\
                 \\
                 4. Phillips. Archimedes the Numerical Analyst (1981) /
                 A summary of Archimedes' work on the computation of
                 $\pi$ using modern notation / 15 \\
                 \\
                 5. Lam and Ang. Circle Measurements in Ancient China
                 (1986) / This paper discusses and contains a
                 translation of Liu Hui's (3rd century) method for
                 evaluating $\pi$ and also examines values for $\pi$
                 given by Zu Chongzhi (429--500) / 20 \\
                 \\
                 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
                 and Solid Figures ($\approx$ 850) / This extract gives
                 an explicit statement and proof that the ratio of the
                 circumference to the diameter is constant / 36 \\
                 \\
                 7. M{\=a}dhava. The Power Series for Arctan and Pi
                 ($\approx$ 1400) / These theorems by a fifteenth
                 century Indian mathematician give Gregory's series for
                 arctan with remainder terms and Leibniz's series for
                 $\pi$ / 45 \\
                 \\
                 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van
                 Ceulen (1938) / Correspondence about van Ceulen's
                 tombstone in reference to it containing some digits of
                 $\pi$ / 51 \\
                 \\
                 9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum
                 Liber VII (1593) / Two excerpts. One containing the
                 first infinite expression of $\pi$, obtained by
                 relating the area of a regular $2n$-gon to that of a
                 regular $n$-gon / 53 \\
                 \\
                 10. Wallis. Computation of $\pi$ by Successive
                 Interpolations (1655) / How Wallis derived the infinite
                 product for $\pi$ that bears his name / 68 \\
                 \\
                 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt
                 including Prop. 189, 191 and an alternate form of the
                 result that gives Wm. Brounker's continued fraction
                 expression for $4/\pi$ / 78 \\
                 \\
                 12. Huygens. De Circuli Magnitudine Inventa (1724) /
                 Huygens's proof of W. Snell's discovery of improvements
                 in Archimedes' method of estimating the lengths of
                 circular arcs / 81 \\
                 \\
                 13. Gregory. Correspondence with John Collins (1671) /
                 A letter to Collins in which he gives his series for
                 arctangent, carried to the ninth power. / 87 \\
                 \\
                 14. Roy. The Discovery of the Series Formula for $\pi$
                 by Leibniz, Gregory, and Nilakantha (1990) / A
                 discussion of the discovery of the series $\pi/4 = 1 -
                 1/3 + 1/5, \cdots{}$ / 92 \\
                 \\
                 15. Jones. The First Use of $\pi$ for the Circle Ratio
                 (1706) / An excerpt from Jones' book, the Synopsis
                 Palmariorum Matheseos: or, a New Introduction to the
                 Mathematics, London, 1706 / 108 \\
                 \\
                 16. Newton. Of the Method of Fluxions and Infinite
                 Series (1737) / An excerpt giving Newton's calculation
                 of $\pi$ to 16 decimal places / 110 \\
                 \\
                 17. Euler. Chapter 10 of Introduction to Analysis of
                 the Infinite (On the Use of the Discovered Fractions to
                 Sum Infinite Series) (1748) / This includes many of
                 Euler's infinite series for $\pi$ and powers of $\pi$ /
                 112 \\
                 \\
                 18. Lambert. M{\'e}moire Sur Quelques
                 Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
                 Transcendentes Circulaires et Logarithmiques (1761) /
                 An excerpt from Lambert's original proof of the
                 irrationality of $\pi$ / 129 \\
                 \\
                 19. Lambert. Irrationality of $\pi$ (1969) / A
                 translation and Struik's discussion of Lambert's proof
                 of the irrationality of $\pi$ / 141 \\
                 \\
                 20. Shanks. Contributions to Mathematics Comprising
                 Chiefly of the Rectification of the Circle to 607
                 Places of Decimals (1853) / Pages from Shank's report
                 of his monumental hand calculation of $\pi$ / 147 \\
                 \\
                 21. Hermite. Sur La Fonction Exponentielle (1873) / The
                 first proof of the transcendence of $e$ / 162 \\
                 \\
                 22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first
                 proof of the transcendence of $\pi$ / 194 \\
                 \\
                 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die
                 Ludolphsche Zahl'' (1885) / Weierstrass' proof of the
                 transcendence of $\pi$ / 207 \\
                 \\
                 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und
                 $\pi$ (1893) / Hilbert's short and elegant
                 simplification of the transcendence proofs for $e$ and
                 $\pi$ / 226 \\
                 \\
                 25. Goodwin. Quadrature of the Circle (1894) / The
                 dubious origin of the attempted legislation of the
                 value of $\pi$ in Indiana / 230 \\
                 \\
                 26. Edington. House Bill No. 246, Indiana State
                 Legislature, 1897 (1935) / A summary of the action
                 taken by the Indiana State Legislature to fix the value
                 of $\pi$ (including a copy of the actual bill that was
                 proposed) / 231 \\
                 \\
                 27. Singmaster. The Legal Values of Pi (1985) / A
                 history of the attempt by Indiana to legislate the
                 value of $\pi$ / 236 \\
                 \\
                 28. Ramanujan. Squaring the Circle (1913) / A geometric
                 approximation to $\pi$ / 240 \\
                 \\
                 29. Ramanujan. Modular Equations and Approximations to
                 $\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that
                 includes a number of striking series and algebraic
                 approximations / 241 \\
                 \\
                 30. Watson. The Marquis and the Land Agent: A Tale of
                 the Eighteenth Century (1933) / A Presidential address
                 to the Mathematical Association in which the author
                 gives an account of ``some of the elementary work on
                 arcs and ellipses and other curves which led up to the
                 idea of inverting an elliptic integral, and so laying
                 the foundations of elliptic functions and doubly
                 periodic functions generally.'' / 258 \\
                 \\
                 31. Ballantine. The Best (?) Formula for Computing
                 $\pi$ to a Thousand Places (1939) / An early attempt to
                 orchestrate the calculation of $\pi$ more cleverly /
                 271 \\
                 \\
                 32. Birch. An Algorithm for Construction of Arctangent
                 Relations (1946) / The object of this note is to
                 express $\pi / 4 $ as a sum of arctan relations in
                 powers of 10 / 274 \\
                 \\
                 33. Niven. A Simple Proof that $\pi$ Is Irrational
                 (1947) / A very concise proof of the irrationality of
                 $\pi$ / 276 \\
                 \\
                 34. Reitwiesner. An ENIAC Determination of $\pi$ and
                 $e$ to 2000 Decimal Places (1950) / One of the first
                 computer-based computations / 277 \\
                 \\
                 35. Schepler. The Chronology of Pi (1950) / A fairly
                 reliable outline of the history of $\pi$ from 3000 BC
                 to 1949 / 282 \\
                 \\
                 36. Mahler. On the Approximation of $\pi$ (1953) /
                 ``The aim of this paper is to determine an explicit
                 lower bound free of unknown constants for the distance
                 of $\pi$ from a given rational or algebraic number'' /
                 306 \\
                 \\
                 37. Wrench, Jr. The Evolution of Extended Decimal
                 Approximations to $\pi$ (1960) / A history of the
                 calculation of the digits of $\pi$ to 1960 \\
                 \\
                 38. Shanks and Wrench, Jr. Calculation of $\pi$ to
                 100,000 Decimals (1962) / A landmark computation of
                 $\pi$ to more than 100,000 places / 326 \\
                 \\
                 39. Sweeny. On the Computation of Euler's Constant
                 (1963) / The computation of Euler's constant to 3566
                 decimal places / 350 \\
                 \\
                 40. Baker. Approximations to the Logarithms of Certain
                 Rational Numbers (1964) / The main purpose of this deep
                 and fundamental paper is to ``deduce results concerning
                 the accuracy with which the natural logarithms of
                 certain rational numbers may be approximated by
                 rational numbers, or, more generally, by algebraic
                 numbers of bounded degree.'' / 359 \\
                 \\
                 41. Adams. Asymptotic Diophantine Approximations to $E$
                 (1966) / An asymptotic estimate for the rational
                 approximation to $e$ which disproves the conjecture
                 that $e$ behaves like almost all numbers in this
                 respect / 368 \\
                 \\
                 42. Mahler. Applications of Some Formulae by Hermite to
                 the Approximations of Exponentials of Logarithms (1967)
                 / An important extension of Hilbert's approach to the
                 study of transcendence / 372 \\
                 \\
                 43. Eves. In Mathematical Circles; A Selection of
                 Mathematical Stories and Anecdotes (excerpt) (1969) / A
                 collection of mathematical stories and anecdotes about
                 $\pi$ / 400 \\
                 \\
                 44. Eves. Mathematical Circles Revisited; A Second
                 Collection of Mathematical Stories and Anecdotes
                 (excerpt) (1971) / A further collection of mathematical
                 stories and anecdotes about $\pi$ / 402 \\
                 \\
                 45. Todd. The Lemniscate Constants (1975) / A unifying
                 account of some of the methods used for computing the
                 lemniscate constants / 412 \\
                 \\
                 46. Salamin. Computation of r Using
                 Arithmetic-Geometric Mean (1976) / The first
                 quadratically converging algorithm for $\pi$ based on
                 Gauss's AGM and on Legendre's relation for elliptic
                 integrals / 418 \\
                 \\
                 47. Brent. Fast Multiple-Precision Evaluation of
                 Elementary Functions (1976) / ``This paper contains the
                 `Gauss-Legendre' method and some different algorithms
                 for log and exp (using Landen transformations).'' / 424
                 \\
                 \\
                 48. Beukers. A Note on the Irrationality of $\zeta(2)$
                 and $\zetq(3)$ (1979) / A short and elegant recasting
                 of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$
                 (and $\zeta(2)$) / 434 \\
                 \\
                 49. van der Poorten. A Proof that Euler Missed \ldots{}
                 Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$
                 (1979) / An illuminating account of Ap{\'e}ry's
                 astonishing proof of the irrationality of $\zeta(3)$ /
                 439 \\
                 \\
                 50. Brent and McMillan. Some New Algorithms for
                 High-Precision Computation of Euler's Constant (1980) /
                 Several new algorithms for high precision calculation
                 of Euler's constant, including one which was used to
                 compute 30,100 decimal places / 448 \\
                 \\
                 51. Apostol. A Proof that Euler Missed: Evaluating
                 $\zeta(2)$ the Easy Way (1983) / This note shows that
                 one of the double integrals considered by Beukers ([48]
                 in the table of contents) can be used to establish
                 directly that $\zeta(2) = \pi / 6$ / 456 \\
                 \\
                 52. O'Shaughnessy. Putting God Back in Math (1983) / An
                 article about the Institute of Pi Research, an
                 organization that ``pokes fun at creationists by
                 pointing out that even the Bible makes mistakes.'' /
                 458 \\
                 \\
                 53. Stern. A Remarkable Approximation to $\pi$ (1985) /
                 Justification of the value of $\pi$ in the Bible
                 through numerological interpretations / 460 \\
                 \\
                 54. Newman and Shanks. On a Sequence Arising in Series
                 for $\pi$ (1984) / More connections between $\pi$ and
                 modular equations / 462 \\
                 \\
                 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984)
                 / An extensive study of the complex analytic properties
                 of the AGM / 481 \\
                 \\
                 56. Borwein and Borwein. The Arithmetic-Geometric Mean
                 and Fast Computation of Elementary Functions (1984) /
                 The relationship between the AGM iteration and fast
                 computation of elementary functions (one of the
                 by-products is an algorithm for $\pi$) / 537 \\
                 \\
                 57. Newman. A Simplified Version of the Fast Algorithms
                 of Brent and Salamin (1984) / Elementary algorithms for
                 evaluating $e^x$ and $\pi$ using the Gauss AGM without
                 explicit elliptic function theory / 553 \\
                 \\
                 58. Wagon. Is Pi Normal? (1985) / A discussion of the
                 conjecture that $\pi$ has randomly distributed digits /
                 557 \\
                 \\
                 59. Keith. Circle Digits: A Self-Referential Story
                 (1986) / A mnemonic for the first 402 decimal places of
                 $\pi$ / 560 \\
                 \\
                 60. Bailey. The Computation of $\pi$ to 29,360,000
                 Decimal Digits Using Borweins' Quartically Convergent
                 Algorithm (1988) / The algorithms used, both for $\pi$
                 and for performing the required multiple-precision
                 arithmetic / 562 \\
                 \\
                 61. Kanada. Vectorization of Multiple-Precision
                 Arithmetic Program and 201,326,000 Decimal Digits of 1
                 Calculation (1988) / Details of the computation and
                 statistical tests of the first 200 million digits of
                 $\pi$ / 576 \\
                 \\
                 62. Borwein and Borwein. Ramanujan and Pi (1988) / This
                 article documents Ramanujan's life, his ingenious
                 approach to calculating $\pi$, and how his approach is
                 now incorporated into modern computer algorithms / 588
                 \\
                 \\
                 63. Chudnovsky and Chudnovsky. Approximations and
                 Complex Multiplication According to Ramanujan (1988) /
                 This excerpt describes ``Ramanujan's original quadratic
                 period--quasiperiod relations for elliptic curves with
                 complex multiplication and their applications to
                 representations of fractions of $\pi$ and other
                 logarithms in terms of rapidly convergent nearly
                 integral (hypergeometric) series.'' / 596 \\
                 \\
                 64. Borwein, Borwein and Bailey. Ramanujan, Modular
                 Equations, and Approximations to Pi or How to Compute
                 One Billion Digits of Pi (1989) / An exposition of the
                 computation of $\pi$ using mathematics rooted in
                 Ramanujan's work / 623 \\
                 \\
                 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers,
                 and Asymptotic Expansions (1989) / An explanation as to
                 why the slowly convergent Gregory series for $\pi$,
                 truncated at 500,000 terms, gives $\pi$ to 40 places
                 with only the 6th, 17th, 18th, and 29th places being
                 incorrect / 642 \\
                 \\
                 66. Beukers, B{\'e}zivin, and Robba. An Alternative
                 Proof of the Lindemann--Weierstrass Theorem (1990) /
                 The Lindemann--Weierstrass theorem as a by-product of a
                 criterion for rationality of solutions of differential
                 equations / 649 \\
                 \\
                 67. Webster. The Tail of Pi (1991) / Various anecdotes
                 about $\pi$ from the 14th annual IMO Lecture to the
                 Royal Society / 654 \\
                 \\
                 68. Eco. An excerpt from Foucault's Pendulum (1993) /
                 ``The unnumbered perfection of the circle itself.'' /
                 658 \\
                 \\
                 69. Keith. Pi Mnemonics and the Art of Constrained
                 Writing (1996) / A mnemonic for $\pi$ based on Edgar
                 Allen Poe's poem ``The Raven.'' / 659 \\
                 \\
                 70. Bailey, Borwein, and Plouffe. On the Rapid
                 Computation of Various Polylogarithmic Constants (1996)
                 / A fast method for computing individual digits of
                 $\pi$ in base 2 / 663 \\
                 Appendix I --- On the Early History of Pi / 677 \\
                 \\
                 Appendix II --- A Computational Chronology of Pi / 683
                 \\
                 \\
                 Appendix III --- Selected Formulae for Pi / 686 \\
                 \\
                 Bibliography / 690 \\
                 \\
                 Credits / 697 \\
                 \\
                 Index / 701",
}

@Book{Berggren:2000:PSB,
  editor =       "Lennart Berggren and Jonathan Borwein and Peter
                 Borwein",
  booktitle =    "Pi: a source book",
  title =        "Pi: a source book",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xx + 736",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4757-3240-5",
  ISBN =         "0-387-98946-3 (hardcover)",
  ISBN-13 =      "978-0-387-98946-4 (hardcover)",
  LCCN =         "QA484 .P5 2000",
  MRclass =      "11-00 (01A05 01A75 11-03)",
  MRnumber =     "1746004",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  libnote =      "Not yet in my library.",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Pi (mathematical constant)",
  tableofcontents = "Preface / v \\
                 \\
                 Preface to the Second Edition / viii \\
                 Acknowledgments / ix \\
                 \\
                 Introduction / xvii \\
                 \\
                 1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$
                 1650 B.C.) / A problem dealing with the area of a round
                 field of given diameter / 1 \\
                 \\
                 2. Engels. Quadrature of the Circle in Ancient Egypt
                 (1977) / A conjectural explanation of how the
                 mathematicians of ancient Egypt approximated the area
                 of a circle / 3 \\
                 \\
                 3. Archimedes. Measurement of a Circle ($\approx$ 250
                 BC) / The seminal work in which Archimedes presents the
                 first true algorithm for $\pi$ / 7 \\
                 \\
                 4. Phillips. Archimedes the Numerical Analyst (1981) /
                 A summary of Archimedes' work on the computation of
                 $\pi$ using modern notation / 15 \\
                 \\
                 5. Lam and Ang. Circle Measurements in Ancient China
                 (1986) / This paper discusses and contains a
                 translation of Liu Hui's (3rd century) method for
                 evaluating $\pi$ and also examines values for $\pi$
                 given by Zu Chongzhi (429--500) / 20 \\
                 \\
                 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
                 and Solid Figures ($\approx$ 850) / This extract gives
                 an explicit statement and proof that the ratio of the
                 circumference to the diameter is constant / 36 \\
                 \\
                 7. M{\=a}dhava. The Power Series for Arctan and Pi
                 ($\approx$ 1400) / These theorems by a fifteenth
                 century Indian mathematician give Gregory's series for
                 arctan with remainder terms and Leibniz's series for
                 $\pi$ / 45 \\
                 \\
                 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van
                 Ceulen (1938) / Correspondence about van Ceulen's
                 tombstone in reference to it containing some digits of
                 $\pi$ / 51 \\
                 \\
                 9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum
                 Liber VII (1593) / Two excerpts. One containing the
                 first infinite expression of $\pi$, obtained by
                 relating the area of a regular $2n$-gon to that of a
                 regular $n$-gon / 53 \\
                 \\
                 10. Wallis. Computation of $\pi$ by Successive
                 Interpolations (1655) / How Wallis derived the infinite
                 product for $\pi$ that bears his name / 68 \\
                 \\
                 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt
                 including Prop. 189, 191 and an alternate form of the
                 result that gives Wm. Brounker's continued fraction
                 expression for $4/\pi$ / 78 \\
                 \\
                 12. Huygens. De Circuli Magnitudine Inventa (1724) /
                 Huygens's proof of W. Snell's discovery of improvements
                 in Archimedes' method of estimating the lengths of
                 circular arcs / 81 \\
                 \\
                 13. Gregory. Correspondence with John Collins (1671) /
                 A letter to Collins in which he gives his series for
                 arctangent, carried to the ninth power. / 87 \\
                 \\
                 14. Roy. The Discovery of the Series Formula for $\pi$
                 by Leibniz, Gregory, and Nilakantha (1990) / A
                 discussion of the discovery of the series $\pi/4 = 1 -
                 1/3 + 1/5, \cdots{}$ / 92 \\
                 \\
                 15. Jones. The First Use of $\pi$ for the Circle Ratio
                 (1706) / An excerpt from Jones' book, the Synopsis
                 Palmariorum Matheseos: or, a New Introduction to the
                 Mathematics, London, 1706 / 108 \\
                 \\
                 16. Newton. Of the Method of Fluxions and Infinite
                 Series (1737) / An excerpt giving Newton's calculation
                 of $\pi$ to 16 decimal places / 110 \\
                 \\
                 17. Euler. Chapter 10 of Introduction to Analysis of
                 the Infinite (On the Use of the Discovered Fractions to
                 Sum Infinite Series) (1748) / This includes many of
                 Euler's infinite series for $\pi$ and powers of $\pi$ /
                 112 \\
                 \\
                 18. Lambert. M{\'e}moire Sur Quelques
                 Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
                 Transcendentes Circulaires et Logarithmiques (1761) /
                 An excerpt from Lambert's original proof of the
                 irrationality of $\pi$ / 129 \\
                 \\
                 19. Lambert. Irrationality of $\pi$ (1969) / A
                 translation and Struik's discussion of Lambert's proof
                 of the irrationality of $\pi$ / 141 \\
                 \\
                 20. Shanks. Contributions to Mathematics Comprising
                 Chiefly of the Rectification of the Circle to 607
                 Places of Decimals (1853) / Pages from Shank's report
                 of his monumental hand calculation of $\pi$ / 147 \\
                 \\
                 21. Hermite. Sur La Fonction Exponentielle (1873) / The
                 first proof of the transcendence of $e$ / 162 \\
                 \\
                 22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first
                 proof of the transcendence of $\pi$ / 194 \\
                 \\
                 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die
                 Ludolphsche Zahl'' (1885) / Weierstrass' proof of the
                 transcendence of $\pi$ / 207 \\
                 \\
                 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und
                 $\pi$ (1893) / Hilbert's short and elegant
                 simplification of the transcendence proofs for $e$ and
                 $\pi$ / 226 \\
                 \\
                 25. Goodwin. Quadrature of the Circle (1894) / The
                 dubious origin of the attempted legislation of the
                 value of $\pi$ in Indiana / 230 \\
                 \\
                 26. Edington. House Bill No. 246, Indiana State
                 Legislature, 1897 (1935) / A summary of the action
                 taken by the Indiana State Legislature to fix the value
                 of $\pi$ (including a copy of the actual bill that was
                 proposed) / 231 \\
                 \\
                 27. Singmaster. The Legal Values of Pi (1985) / A
                 history of the attempt by Indiana to legislate the
                 value of $\pi$ / 236 \\
                 \\
                 28. Ramanujan. Squaring the Circle (1913) / A geometric
                 approximation to $\pi$ / 240 \\
                 \\
                 29. Ramanujan. Modular Equations and Approximations to
                 $\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that
                 includes a number of striking series and algebraic
                 approximations / 241 \\
                 \\
                 30. Watson. The Marquis and the Land Agent: A Tale of
                 the Eighteenth Century (1933) / A Presidential address
                 to the Mathematical Association in which the author
                 gives an account of ``some of the elementary work on
                 arcs and ellipses and other curves which led up to the
                 idea of inverting an elliptic integral, and so laying
                 the foundations of elliptic functions and doubly
                 periodic functions generally.'' / 258 \\
                 \\
                 31. Ballantine. The Best (?) Formula for Computing
                 $\pi$ to a Thousand Places (1939) / An early attempt to
                 orchestrate the calculation of $\pi$ more cleverly /
                 271 \\
                 \\
                 32. Birch. An Algorithm for Construction of Arctangent
                 Relations (1946) / The object of this note is to
                 express $\pi / 4 $ as a sum of arctan relations in
                 powers of 10 / 274 \\
                 \\
                 33. Niven. A Simple Proof that $\pi$ Is Irrational
                 (1947) / A very concise proof of the irrationality of
                 $\pi$ / 276 \\
                 \\
                 34. Reitwiesner. An ENIAC Determination of $\pi$ and
                 $e$ to 2000 Decimal Places (1950) / One of the first
                 computer-based computations / 277 \\
                 \\
                 35. Schepler. The Chronology of Pi (1950) / A fairly
                 reliable outline of the history of $\pi$ from 3000 BC
                 to 1949 / 282 \\
                 \\
                 36. Mahler. On the Approximation of $\pi$ (1953) /
                 ``The aim of this paper is to determine an explicit
                 lower bound free of unknown constants for the distance
                 of $\pi$ from a given rational or algebraic number'' /
                 306 \\
                 \\
                 37. Wrench, Jr. The Evolution of Extended Decimal
                 Approximations to $\pi$ (1960) / A history of the
                 calculation of the digits of $\pi$ to 1960 \\
                 \\
                 38. Shanks and Wrench, Jr. Calculation of $\pi$ to
                 100,000 Decimals (1962) / A landmark computation of
                 $\pi$ to more than 100,000 places / 326 \\
                 \\
                 39. Sweeny. On the Computation of Euler's Constant
                 (1963) / The computation of Euler's constant to 3566
                 decimal places / 350 \\
                 \\
                 40. Baker. Approximations to the Logarithms of Certain
                 Rational Numbers (1964) / The main purpose of this deep
                 and fundamental paper is to ``deduce results concerning
                 the accuracy with which the natural logarithms of
                 certain rational numbers may be approximated by
                 rational numbers, or, more generally, by algebraic
                 numbers of bounded degree.'' / 359 \\
                 \\
                 41. Adams. Asymptotic Diophantine Approximations to $E$
                 (1966) / An asymptotic estimate for the rational
                 approximation to $e$ which disproves the conjecture
                 that $e$ behaves like almost all numbers in this
                 respect / 368 \\
                 \\
                 42. Mahler. Applications of Some Formulae by Hermite to
                 the Approximations of Exponentials of Logarithms (1967)
                 / An important extension of Hilbert's approach to the
                 study of transcendence / 372 \\
                 \\
                 43. Eves. In Mathematical Circles; A Selection of
                 Mathematical Stories and Anecdotes (excerpt) (1969) / A
                 collection of mathematical stories and anecdotes about
                 $\pi$ / 400 \\
                 \\
                 44. Eves. Mathematical Circles Revisited; A Second
                 Collection of Mathematical Stories and Anecdotes
                 (excerpt) (1971) / A further collection of mathematical
                 stories and anecdotes about $\pi$ / 402 \\
                 \\
                 45. Todd. The Lemniscate Constants (1975) / A unifying
                 account of some of the methods used for computing the
                 lemniscate constants / 412 \\
                 \\
                 46. Salamin. Computation of r Using
                 Arithmetic-Geometric Mean (1976) / The first
                 quadratically converging algorithm for $\pi$ based on
                 Gauss's AGM and on Legendre's relation for elliptic
                 integrals / 418 \\
                 \\
                 47. Brent. Fast Multiple-Precision Evaluation of
                 Elementary Functions (1976) / ``This paper contains the
                 `Gauss-Legendre' method and some different algorithms
                 for log and exp (using Landen transformations).'' / 424
                 \\
                 \\
                 48. Beukers. A Note on the Irrationality of $\zeta(2)$
                 and $\zetq(3)$ (1979) / A short and elegant recasting
                 of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$
                 (and $\zeta(2)$) / 434 \\
                 \\
                 49. van der Poorten. A Proof that Euler Missed \ldots{}
                 Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$
                 (1979) / An illuminating account of Ap{\'e}ry's
                 astonishing proof of the irrationality of $\zeta(3)$ /
                 439 \\
                 \\
                 50. Brent and McMillan. Some New Algorithms for
                 High-Precision Computation of Euler's Constant (1980) /
                 Several new algorithms for high precision calculation
                 of Euler's constant, including one which was used to
                 compute 30,100 decimal places / 448 \\
                 \\
                 51. Apostol. A Proof that Euler Missed: Evaluating
                 $\zeta(2)$ the Easy Way (1983) / This note shows that
                 one of the double integrals considered by Beukers ([48]
                 in the table of contents) can be used to establish
                 directly that $\zeta(2) = \pi / 6$ / 456 \\
                 \\
                 52. O'Shaughnessy. Putting God Back in Math (1983) / An
                 article about the Institute of Pi Research, an
                 organization that ``pokes fun at creationists by
                 pointing out that even the Bible makes mistakes.'' /
                 458 \\
                 \\
                 53. Stern. A Remarkable Approximation to $\pi$ (1985) /
                 Justification of the value of $\pi$ in the Bible
                 through numerological interpretations / 460 \\
                 \\
                 54. Newman and Shanks. On a Sequence Arising in Series
                 for $\pi$ (1984) / More connections between $\pi$ and
                 modular equations / 462 \\
                 \\
                 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984)
                 / An extensive study of the complex analytic properties
                 of the AGM / 481 \\
                 \\
                 56. Borwein and Borwein. The Arithmetic-Geometric Mean
                 and Fast Computation of Elementary Functions (1984) /
                 The relationship between the AGM iteration and fast
                 computation of elementary functions (one of the
                 by-products is an algorithm for $\pi$) / 537 \\
                 \\
                 57. Newman. A Simplified Version of the Fast Algorithms
                 of Brent and Salamin (1984) / Elementary algorithms for
                 evaluating $e^x$ and $\pi$ using the Gauss AGM without
                 explicit elliptic function theory / 553 \\
                 \\
                 58. Wagon. Is Pi Normal? (1985) / A discussion of the
                 conjecture that $\pi$ has randomly distributed digits /
                 557 \\
                 \\
                 59. Keith. Circle Digits: A Self-Referential Story
                 (1986) / A mnemonic for the first 402 decimal places of
                 $\pi$ / 560 \\
                 \\
                 60. Bailey. The Computation of $\pi$ to 29,360,000
                 Decimal Digits Using Borweins' Quartically Convergent
                 Algorithm (1988) / The algorithms used, both for $\pi$
                 and for performing the required multiple-precision
                 arithmetic / 562 \\
                 \\
                 61. Kanada. Vectorization of Multiple-Precision
                 Arithmetic Program and 201,326,000 Decimal Digits of 1
                 Calculation (1988) / Details of the computation and
                 statistical tests of the first 200 million digits of
                 $\pi$ / 576 \\
                 \\
                 62. Borwein and Borwein. Ramanujan and Pi (1988) / This
                 article documents Ramanujan's life, his ingenious
                 approach to calculating $\pi$, and how his approach is
                 now incorporated into modern computer algorithms / 588
                 \\
                 \\
                 63. Chudnovsky and Chudnovsky. Approximations and
                 Complex Multiplication According to Ramanujan (1988) /
                 This excerpt describes ``Ramanujan's original quadratic
                 period--quasiperiod relations for elliptic curves with
                 complex multiplication and their applications to
                 representations of fractions of $\pi$ and other
                 logarithms in terms of rapidly convergent nearly
                 integral (hypergeometric) series.'' / 596 \\
                 \\
                 64. Borwein, Borwein and Bailey. Ramanujan, Modular
                 Equations, and Approximations to Pi or How to Compute
                 One Billion Digits of Pi (1989) / An exposition of the
                 computation of $\pi$ using mathematics rooted in
                 Ramanujan's work / 623 \\
                 \\
                 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers,
                 and Asymptotic Expansions (1989) / An explanation as to
                 why the slowly convergent Gregory series for $\pi$,
                 truncated at 500,000 terms, gives $\pi$ to 40 places
                 with only the 6th, 17th, 18th, and 29th places being
                 incorrect / 642 \\
                 \\
                 66. Beukers, B{\'e}zivin, and Robba. An Alternative
                 Proof of the Lindemann--Weierstrass Theorem (1990) /
                 The Lindemann--Weierstrass theorem as a by-product of a
                 criterion for rationality of solutions of differential
                 equations / 649 \\
                 \\
                 67. Webster. The Tail of Pi (1991) / Various anecdotes
                 about $\pi$ from the 14th annual IMO Lecture to the
                 Royal Society / 654 \\
                 \\
                 68. Eco. An excerpt from Foucault's Pendulum (1993) /
                 ``The unnumbered perfection of the circle itself.'' /
                 658 \\
                 \\
                 69. Keith. Pi Mnemonics and the Art of Constrained
                 Writing (1996) / A mnemonic for $\pi$ based on Edgar
                 Allen Poe's poem ``The Raven.'' / 659 \\
                 \\
                 70. Bailey, Borwein, and Plouffe. On the Rapid
                 Computation of Various Polylogarithmic Constants (1996)
                 / A fast method for computing individual digits of
                 $\pi$ in base 2 / 663 \\
                 Appendix I --- On the Early History of Pi / 677 \\
                 \\
                 Appendix II --- A Computational Chronology of Pi / 683
                 \\
                 \\
                 Appendix III --- Selected Formulae for Pi / 686 \\
                 \\
                 Appendix IV --- Translations of Vi{\`e}te and Huygens /
                 690 \\
                 Bibliography / 711 \\
                 \\
                 Credits / 717 \\
                 \\
                 Index / 721",
}

@Book{Berggren:2004:PSB,
  editor =       "Lennart Berggren and Jonathan Borwein and Peter
                 Borwein",
  booktitle =    "Pi: a source book",
  title =        "Pi: a source book",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Third",
  pages =        "xx + 797",
  year =         "2004",
  DOI =          "https://doi.org/10.1007/978-1-4757-4217-6",
  ISBN =         "0-387-20571-3",
  ISBN-13 =      "978-0-387-20571-7",
  MRclass =      "11-00 (01A05 01A75 11-03)",
  MRnumber =     "2065455",
  MRreviewer =   "F. Beukers",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 2003:210.",
  tableofcontents = "Preface to the Third Edition / v \\
                 Preface to the Second Edition / vi \\
                 Preface / vii \\
                 Acknowledgments / x \\
                 Introduction / xvii \\
                 1. The Rhind Mathematical Papyrus --- Problem 50
                 ($\approx$1650 B.C.) / A problem dealing with the area
                 of a round field of given diameter / 1 \\
                 2. Engels / Quadrature of the Circle in Ancient Egypt
                 (1977) / A conjectural explanation of how the
                 mathematicians of ancient Egypt approximated the area
                 of a circle / 3 \\
                 3. Archimedes / Measurement of a Circle --- (-250 B.C.)
                 / The seminal work in which Archimedes presents the
                 first true algorithm for $ \pi $ / 7 \\
                 4. Phillips / Archimedes the Numerical --- Analyst
                 (1981) / A summary of Archimedes' work on the
                 computation of $ \pi $ using modem notation / 15 \\
                 5. Lam and Ang / Circle Measurements in Ancient China
                 (1986) / This paper discusses and contains a
                 translation of Liu Hui's (3rd century) method for
                 evaluating $ \pi $ and also examines values for $ \pi $
                 given by Zu Chongzhi (429--500) / 20 \\
                 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
                 and Solid Figures (--850) / This extract gives an
                 explicit statement and proof that the ratio of the
                 circumference to the diameter is constant / 36 \\
                 7. M{\=a}dhava / The Power Series for Arctan and Pi
                 (-1400) / These theorems by a fifteenth century Indian
                 mathematician give Gregory's series for arctan with
                 remainder terms and Leibniz's series for $ \pi $ / 45
                 \\
                 8. Hope-Jones / Ludolph (or Ludolff or Lucius) van
                 Ceulen (1938) / Correspondence about van Ceulen's
                 tombstone in reference to it containing some digits of
                 $ \pi $ / 51 \\
                 9. Vi{\`e}te / \booktitle{Variorum de Rebus
                 Mathematicis Reponsorum Liber VII} (1593) / Two
                 excerpts. One containing the first infinite expression
                 of $ \pi $, obtained by relating the area of a regular
                 $2n$-gon to that of a regular $n$-gon / 53 \\
                 10. Wallis. Computation of $ \pi $ by Successive
                 Interpolations (1655) / How Wallis derived the infinite
                 product for $ \pi $ that bears his name / 68 \\
                 11. Wallis / \booktitle{Arithmetica Infinitorum} (1655)
                 / An excerpt including Prop. 189, 191 and an alternate
                 form of the result that gives Wm. Brounker's continued
                 fraction expression for $ 4 / \pi$ / ?? \\
                 12. Huygens / \booktitle{De Circuli Magnitudine
                 Inventa} (1654) / Huygens's demonstration of how to
                 triple the number of correct decimals over those in
                 Archimedes' estimate of $ \pi $ / 81 13. Gregory /
                 Correspondence with John Collins (1671) / A letter to
                 Collins in which he gives his series for arctangent,
                 carried to the ninth power / 87 \\
                 14. Roy / The Discovery of the Series Formula for $ \pi
                 $ by Leibniz, Gregory, and Nilakantha (1990) / A
                 discussion of the discovery of the series $ \pi / 4 = 1
                 - 1/3 + 1/5 - \cdots{} $ / 92 \\
                 15. Jones / The First Use of $ \pi $ for the Circle
                 Ratio (1706) / An excerpt from Jones' book, the
                 \booktitle{Synopsis Palmariorum Matheseos: or, a New
                 Introduction to the Mathematics}, London, 1706 / 108
                 \\
                 16. Newton / Of the Method of Fluxions and Infinite
                 Series (1737) / An excerpt giving Newton's calculation
                 of $ \pi $ to 16 decimal places / 110 \\
                 17. Euler / Chapter 10 of \booktitle{Introduction to
                 Analysis of the Infinite (On the Use of the Discovered
                 Fractions to Sum Infinite Series)} (1748) / This
                 includes many of Euler's infinite series for $ \pi $
                 and powers of $ \pi $ / 112 \\
                 18. Lambert / \booktitle{M{\'e}moire Sur Quelques
                 Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
                 Transcendentes Circulaires et Logarithmiques} (1761) /
                 An excerpt from Lambert's original proof of the
                 irrationality of $ \pi $ / 129 19. Lambert /
                 Irrationality of $ \pi $ (1969) / A translation and
                 Struik's discussion of Lambert's proof of the
                 irrationality of $ \pi $ / 141 \\
                 20. Shanks / Contributions to Mathematics Comprising
                 Chiefly of the Rectification of the Circle to 607
                 Places of Decimals (1853) / Pages from Shanks's report
                 of his monumental hand calculation of $ \pi $ / 147 \\
                 21. Hermite / \booktitle{Sur La Fonction Exponentielle}
                 (1873) / The first proof of the transcendence of $ e $
                 / 162 \\
                 22. Lindemann / \booktitle{Ueber die Zahl $ \pi $}
                 (1882) / The first proof of the transcendence of $ \pi
                 $ / 194 23. Weierstrass / \booktitle{Zu Lindemann's
                 Abhandlung ``{\"U}ber die Ludolphsche Zahl''} (1885) /
                 Weierstrass' proof of the transcendence of $ \pi $ /
                 207 24. Hilbert / \booktitle{Ueber die Transzendenz der
                 Zahlen $ e $ und $ \pi $} (1893) / Hilbert's short and
                 elegant simplification of the transcendence proofs for
                 $ e $ and $ \pi $ / 226 25. Goodwin / Quadrature of the
                 Circle (1894) / The dubious origin of the attempted
                 legislation of the value of $ \pi $ in Indiana / 230
                 \\
                 26. Edington / House Bill No. 246, Indiana State
                 Legislature, 1897 (1935) / A summary of the action
                 taken by the Indiana State Legislature to fix the value
                 of $ \pi $ (including a copy of the actual bill that
                 was proposed) / 231 \\
                 27. Singmaster / The Legal Values of Pi (1985) / A
                 history of the attempt by Indiana to legislate the
                 value of $ \pi $ / 236 \\
                 28. Ramanujan / Squaring the Circle (1913) / A
                 geometric approximation to $ \pi $ / 240 \\
                 29. Ramanujan / Modular Equations and Approximations to
                 $ \pi $ (1914) / Ramanujan's seminal paper on pi that
                 includes a number of striking series and algebraic
                 approximations / 241 \\
                 30. Watson / The Marquis and the Land Agent: A Tale of
                 the Eighteenth Century (1933) / A Presidential address
                 to the Mathematical Association in which the author
                 gives an account of ``some of the elementary work on
                 arcs and ellipses and other curves which led up to the
                 idea of inverting an elliptic integral, and so laying
                 the foundations of elliptic functions and doubly
                 periodic functions generally.'' / ?? \\
                 31. Ballantine / The Best (?) Formula for Computing $
                 \pi $ to a Thousand Places (1939) / An early attempt to
                 orchestrate the calculation of $ \pi $ more cleverly /
                 271 \\
                 32. Birch / An Algorithm for Construction of Arctangent
                 Relations (1946) / The object of this note is to
                 express $ \pi / 4$ as a sum of arctan relations in
                 powers of 10 / 274 \\
                 33. Niven / A Simple Proof that $ \pi $ is Irrational
                 (1947) / A very concise proof of the irrationality of $
                 \pi $ / 276 \\
                 34. Reitwiesner / An ENIAC Determination of $ \pi $ and
                 $ e $ to 2000 Decimal Places (1950) / One of the first
                 computer-based computations / 277 \\
                 35. Schepler / The Chronology of Pi (1950) / A fairly
                 reliable outline of the history of $ \pi $ from 3000
                 B.C. to 1949 / 282 \\
                 36. Mahler / On the Approximation of $ \pi $ (1953) /
                 ``The aim of this paper is to determine an explicit
                 lower bound free of unknown constants for the distance
                 of $ \pi $ from a given rational or algebraic number.''
                 / 306 \\
                 37. Wrench, Jr. / The Evolution of Extended Decimal
                 Approximations to $ \pi $ (1960) / A history of the
                 calculation of the digits of $ \pi $ to 1960 / 319 \\
                 38. Shanks and Wrench, Jr. / Calculation of $ \pi $ to
                 100,000 Decimals (1962) / A landmark computation of $
                 \pi $ to more than 100,000 places / 326 39. Sweeny / On
                 the Computation of Euler's Constant (1963) / The
                 computation of Euler's constant to 3566 decimal places
                 / 350 40. Baker / Approximations to the Logarithms of
                 Certain Rational Numbers (1964) / The main purpose of
                 this deep and fundamental paper is to ``deduce results
                 concerning the accuracy with which the natural
                 logarithms of certain rational numbers may be
                 approximated by rational numbers, or, more generally,
                 by algebraic numbers of bounded degree.'' / 359 \\
                 41. Adams / Asymptotic Diophantine Approximations to e
                 (1966) / An asymptotic estimate for the rational
                 approximation to $ e $ which disproves the conjecture
                 that $ e $ behaves like almost all numbers in this
                 respect / 368 \\
                 42. Mahler / Applications of Some Formulae by Hermite
                 to the Approximations of Exponentials of Logarithms
                 (1967) / An important extension of Hilbert's approach
                 to the study of transcendence / 372 43. Eves / In
                 Mathematical Circles; A Selection of Mathematical
                 Stories and Anecdotes (excerpt) (1969) / A collection
                 of mathematical stories and anecdotes about $ \pi $ /
                 456 \\
                 44. Eves / Mathematical Circles Revisited; A Second
                 Collection of Mathematical Stories and Anecdotes
                 (excerpt) (1971) / A further collection of mathematical
                 stories and anecdotes about $ \pi $ / 402 45. Todd /
                 The Lemniscate Constants (1975) / A unifying account of
                 some of the methods used for computing the lemniscate
                 constants / 412 \\
                 46. Salamin / Computation of $ \pi $ Using
                 Arithmetic--Geometric Mean (1976) / The first
                 quadratically converging algorithm for $ \pi $ based on
                 Gauss's AGM and on Legendre's relation for elliptic
                 integrals / 418 \\
                 47. Brent / Fast Multiple-Precision Evaluation of
                 Elementary Functions (1976) / ``This paper contains the
                 `Gauss--Legendre' method and some different algorithms
                 for $\log$ and $\exp$ (using Landen transformations).''
                 / 424 \\
                 48. Beukers / A Note on the Irrationality of $ \zeta(2)
                 $ and $ \zeta(3) $ (1979) / A short and elegant
                 recasting of Apery's proof of the irrationality of
                 $\zeta(3)$ (and $\zeta(2)$) / 434 \\
                 49. van der Poorten / A Proof that Euler Missed
                 \ldots{} Apery's Proof of the Irrationality of $\zeta
                 (3)$ (1979) / An illuminating account of Apery's
                 astonishing proof of the irrationality of $\zeta (3)$ /
                 439 \\
                 50. Brent and McMillan / Some New Algorithms for
                 High-Precision Computation of Euler's Constant (1980) /
                 Several new algorithms for high-precision calculation
                 of Euler's constant, including one which was used to
                 compute 30,100 decimal places / 448 \\
                 51. Apostol / A Proof that Euler Missed: Evaluating
                 $\zeta(2)$ the Easy Way (1983) / This note shows that
                 one of the double integrals considered by Beukers ([48]
                 in the table of contents) can be used to establish
                 directly that $\zeta(2) = \pi^2 / 6$ / 456 \\
                 52. O'Shaughnessy / Putting God Back in Math (1983) /
                 An article about the Institute of Pi Research, an
                 organization that ``pokes fun at creationists by
                 pointing out that even the Bible makes mistakes.'' /
                 458 \\
                 53. Stern / A Remarkable Approximation to $ \pi $
                 (1985) / Justification of the value of $ \pi $ in the
                 Bible through numerological interpretations / 460 \\
                 54. Newman and Shanks / On a Sequence Arising in Series
                 for $ \pi $ (1984) / More connections between $ \pi $
                 and modular equations / 462 \\
                 55. Cox / The Arithmetic--Geometric Mean of Gauss
                 (1984) / An extensive study of the complex analytic
                 properties of the AGM / 481 \\
                 56. Borwein and Borwein / The Arithmetic--Geometric
                 Mean and Fast Computation of Elementary Functions
                 (1984) / The relationship between the AGM iteration and
                 fast computation of elementary functions (one of the
                 by-products is an algorithm for $ \pi $) / 537 57.
                 Newman / A Simplified Version of the Fast Algorithms of
                 Brent and Salamin (1984) / Elementary algorithms for
                 evaluating $ e^x $ and $ \pi $ using the Gauss AGM
                 without explicit elliptic function theory / 553 \\
                 58. Wagon / Is Pi Normal? (1985) / A discussion of the
                 conjecture that $ \pi $ has randomly distributed digits
                 / 557 \\
                 59. Keith / Circle Digits: A Self-Referential Story
                 (1986) / A mnemonic for the first 402 decimal places of
                 $ \pi $ / 560 \\
                 60. Bailey / The Computation of $ \pi $ to 29,360,000
                 Decimal Digits Using Borwein's Quartically Convergent
                 Algorithm (1988) / The algorithms used, both for $ \pi
                 $ and for performing the required multiple-precision
                 arithmetic / 562 \\
                 61. Kanada / Vectorization of Multiple-Precision
                 Arithmetic Program and 201,326,000 Decimal Digits of $
                 \pi $ Calculation (1988) / Details of the computation
                 and statistical tests of the first 200 million digits
                 of $ \pi $ / 576 \\
                 62. Borwein and Borwein / Ramanujan and Pi (1988) /
                 This article documents Ramanujan's life, his ingenious
                 approach to calculating $ \pi $, and how his approach
                 is now incorporated into modern computer algorithms /
                 588 \\
                 63. Chudnovsky and Chudnovsky / Approximations and
                 Complex Multiplication According to Ramanujan (1988) /
                 This excerpt describes ``Ramanujan's original quadratic
                 period--quasiperiod relations for elliptic curves with
                 complex multiplication and their applications to
                 representations of fractions of $ \pi $ and other
                 logarithms in terms of rapidly convergent nearly
                 integral (hypergeometric) series.'' / 596 \\
                 64. Borwein, Borwein and Bailey / Ramanujan, Modular
                 Equations, and Approximations to Pi or How to Compute
                 One Billion Digits of Pi (1989) / An exposition of the
                 computation of $ \pi $ using mathematics rooted in
                 Ramanujan's work / 623 \\
                 65. Borwein, Borwein and Dilcher / Pi, Euler Numbers,
                 and Asymptotic Expansions (1989) / An explanation as to
                 why the slowly convergent Gregory series for $ \pi $,
                 truncated at 500,000 terms, gives $ \pi $ to 40 places
                 with only the 6th, 17th, 18th, and 29th places being
                 incorrect / 642 \\
                 66. Beukers, Bezivin, and Robba / An Alternative Proof
                 of the Lindemann--Weierstrass Theorem (1990) / The
                 Lindemann--Weierstrass theorem as a by-product of a
                 criterion for rationality of solutions of differential
                 equations / 649 \\
                 67. Webster / The Tale of Pi (1991) / Various anecdotes
                 about $ \pi $ from the 14th annual IMO Lecture to the
                 Royal Society / 654 \\
                 68. Eco / An excerpt from Foucault's Pendulum (1993) /
                 ``The unnumbered perfection of the circle itself.'' /
                 658 \\
                 69. Keith / Pi Mnemonics and the Art of Constrained
                 Writing (1996) / A mnemonic for $ \pi $ based on Edgar
                 Allen Poe's poem ``The Raven.'' / 659 \\
                 70. Bailey, Borwein, and Plouffe / On the Rapid
                 Computation of Various Polylogarithmic Constants (1997)
                 / A fast method for computing individual digits of $
                 \pi $ in base 2 / 663 \\
                 Appendix I --- On the Early History of Pi / 677 \\
                 Appendix II --- A Computational Chronology of Pi / 683
                 \\
                 Appendix III --- Selected Formulae for Pi / 686 \\
                 Appendix IV --- Translations of Viele and Huygens / 690
                 \\
                 Bibliography / 710 \\
                 Credits / 717 \\
                 A Pamphlet on Pi / 721 \\
                 Contents / 723 \\
                 1. Pi and Its Friends / 725 \\
                 2. Normality of Numbers / 741 \\
                 3. Historia Cyclometrica / 753 \\
                 4. Demotica Cyclometrica / 771 \\
                 References / 779 \\
                 Index / 783",
}

@Book{Arndt:2011:MC,
  author =       "J{\"o}rg Arndt",
  booktitle =    "Matters Computational",
  title =        "Matters Computational",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiv + 966",
  year =         "2011",
  DOI =          "https://doi.org/10.1007/978-3-642-14764-7",
  ISBN =         "3-642-14764-X, 3-642-14763-1",
  ISBN-13 =      "978-3-642-14764-7, 978-3-642-14763-0",
  LCCN =         "QA9.58 .A76 2011",
  bibdate =      "Tue Mar 14 15:06:32 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  abstract =     "This book provides algorithms and ideas for
                 computationalists. Subjects treated include low-level
                 algorithms, bit wizardry, combinatorial generation,
                 fast transforms like the Fourier transform, and fast
                 arithmetic for both real numbers and finite fields.
                 Various optimization techniques are described and the
                 actual performance of many given implementations is
                 examined. The focus is on material that does not
                 usually appear in textbooks on algorithms. The
                 implementations are done in C++ and the GP language,
                 written for POSIX-compliant platforms such as the Linux
                 and BSD operating systems.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Matters Computational \\
                 Preface \\
                 Contents \\
                 Part I: Low level algorithms \\
                 Part II:Combinatorial generation \\
                 Part III:Fast transforms \\
                 Part IV: Fast arithmetic \\
                 Part V: Algorithms for finite fields \\
                 Appendix A: The electronic version of the book \\
                 Appendix B: Machine used for benchmarking \\
                 Appendix C: The GP language \\
                 Bibliography \\
                 Index",
  subject =      "Mathematics",
  tableofcontents = "Low level algorithms \\
                 Bit wizardry / 2--101 \\
                 Permutations and their operations / 102--133 \\
                 Sorting and searching / 134--152 \\
                 Data structures / 153--170 \\
                 Combinatorial generation \\
                 Conventions and considerations / 172--175 \\
                 Combinations / 176--193 \\
                 Compositions / 194--201 \\
                 Subsets / 202--216 \\
                 Mixed radix numbers / 217--231 \\
                 Permutations / 232--276 \\
                 Permutations with special properties / 277--290 \\
                 $k$-permutations / 291--294 \\
                 Multisets / 295--303 \\
                 Gray codes for string with restrictions / 304--322 \\
                 Parenthesis strings / 323--338 \\
                 Integer partitions / 339--353 \\
                 Set partitions / 354--369 \\
                 Necklaces and Lyndon words / 370--383 \\
                 Hadamard and conference matrices / 384--390 \\
                 Searching paths in directed graphs / 391--408 \\
                 Fast transforms \\
                 The Fourier transform / 410--439 \\
                 Convolution, correlation, and more FFT algorithms /
                 440--458 \\
                 The Walsh transform and its relatives / 459--496 \\
                 The Haar transform / 497--514 \\
                 The Hartley transform / 515--534 \\
                 Number theoretic transforms (NTTs) / 535--542 \\
                 Fast wavelet transforms / 543--548 \\
                 Fast arithmetic \\
                 Fast multiplication and exponentiation / 550--566 \\
                 Root extraction / 567--586 \\
                 Iterations for the inversion of a function / 587--598
                 \\
                 The AGM, elliptic integrals, and algorithms for
                 computing / 599--621 \\
                 Logarithm and exponential function / 622--640 \\
                 Computing the elementary functions with limited
                 resources / 641--650 \\
                 Numerical evaluation of power series / 651--665 \\
                 Recurrences and Chebyshev polynomials / 666--684 \\
                 Hypergeometric series / 685--703 \\
                 Cyclotomic polynomials, product forms, and continued
                 fractions / 704--725 \\
                 Synthetic Iterations / 726--762 \\
                 Algorithms for finite fields \\
                 Modular arithmetic and some number theory / 764--821
                 \\
                 Binary polynomials / 822--863 \\
                 Shift registers / 864--885 \\
                 Binary finite fields: $ {\rm GF}(2^n) $ / 886--920 \\
                 The electronic version of the book \\
                 Machine used for benchmarking \\
                 The GP language \\
                 Bibliography \\
                 Index",
}

@Book{Bailey:2016:PNG,
  editor =       "David H. Bailey and Jonathan M. Borwein",
  booktitle =    "Pi: the next generation: a sourcebook on the recent
                 history of Pi and its computation",
  title =        "Pi: the next generation: a sourcebook on the recent
                 history of Pi and its computation",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiv + 507",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0",
  ISBN =         "3-319-32375-X, 3-319-32377-6 (e-book)",
  ISBN-13 =      "978-3-319-32375-6, 978-3-319-32377-0 (e-book)",
  LCCN =         "QA251",
  MRclass =      "01A75, 11-00, 65-00, 11-06, 65-06",
  bibdate =      "Fri Sep 30 09:43:05 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1716/;
                 http://lib.myilibrary.com?id=941862",
  ZMnumber =     "1342.01042",
  acknowledgement = ack-nhfb,
  subject =      "Pi",
  tableofcontents = "Computation of $\pi$ using arithmetic--geometric
                 mean (1976) / Salamin, Eugene / 1--8 \\
                 Fast multiple-precision evaluation of elementary
                 functions (1976) / Brent, Richard P. / 9--20 \\
                 The arithmetic--geometric mean of Gauss (1984) / Cox,
                 David A. / 21--78 \\
                 The arithmetic--geometric mean and fast computation of
                 elementary functions (1984) / Borwein, J. M. and
                 Borwein, P. B. / 79--96 \\
                 A simplified version of the fast algorithms of Brent
                 and Salamin (1985) / Newman, D. J. / 97--102 \\
                 Is pi normal? (1985) / Wagon, S. / 103--107 \\
                 The computation of $\pi$ to 29,360,000 decimal digits
                 using Borweins' quartically convergent algorithm (1988)
                 / Bailey, David H. / 109--124 \\
                 Gauss, Landen, Ramanujan, the arithmetic--geometric
                 mean, ellipses, $\pi$, and the Ladies Diary (1988) /
                 Almkvist, Gert (et al.) / 125--150 \\
                 Vectorization of multiple-precision arithmetic program
                 and 201,326,000 decimal digits of pi calculation (1988)
                 / Kanada, Yasumasa / 151--164 \\
                 Ramanujan and pi (1988) / Borwein, Jonathan M. (et al.)
                 / 165--174 \\
                 Ramanujan, modular equations, and approximations to pi
                 or how to compute one billion digits of pi (1989) /
                 Borwein, Jonathan M. (et al.) / 175--195 \\
                 Pi, Euler numbers, and asymptotic expansions (1989) /
                 Borwein, Jonathan M. (et al.) / 197--205 \\
                 A spigot algorithm for the digits of $\pi$ (1995) /
                 Rabinowitz, Stanley (et al.) / 207--217 \\
                 On the rapid computation of various polylogarithmic
                 constants (1997) / Bailey, David H. (et al.) / 219--231
                 \\
                 Similarities in irrationality proofs for $\pi$, ln 2,
                 \zeta(2), and \zeta(3) (2001) / Huylebrouck, Dirk /
                 233--244 \\
                 Unbounded spigot algorithms for the digits of pi (2006)
                 / Gibbons, Jeremy / 245--257 \\
                 Mathematics by experiment: Plausible reasoning in the
                 21st Century (2008) / Bailey, David H. (et al.) /
                 259--291 \\
                 Approximations to $\pi$ derived from integrals with
                 nonnegative integrands (2009) / Lucas, Stephen K. /
                 293--301 \\
                 Ramanujan's series for 1/$\pi$: A survey (2009) /
                 Baruah, Nayandeep Deka (et al.) / 303--325 \\
                 The computation of previously inaccessible digits of
                 $\pi$ / Bailey, David H. (et al.) / 327--339 \\
                 Walking on real numbers (2013) / Artacho, Francisco J.
                 Arag{\'o}n (et al.) / 341--361 \\
                 Birth, growth and computation of pi to ten trillion
                 digits (2013) / Agarwal, Ravi (et al.) / 363--423 \\
                 Pi day is upon us again and we still do not know if pi
                 is normal (2014) / Bailey, David H. (et al.) / 425--442
                 \\
                 The Life of $\pi$ (2014) / Borwein, Jonathan M. (et
                 al.) / 443--474 \\
                 I prefer pi: A brief history and anthology of articles
                 in the American Mathematical Monthly (2015) / Borwein,
                 Jonathan M. / 475--499",
}

@Proceedings{Bailey:2020:AVC,
  editor =       "David H. Bailey and Naomi Simone Borwein and Richard
                 P. Brent and Regina S. Burachik and Judy-anne Heather
                 Osborn and Brailey Sims and Qiji J. Zhu",
  booktitle =    "From Analysis to Visualization: A Celebration of the
                 Life and Legacy of {Jonathan M. Borwein, Callaghan,
                 Australia, September 2017}",
  title =        "From Analysis to Visualization: A Celebration of the
                 Life and Legacy of {Jonathan M. Borwein, Callaghan,
                 Australia, September 2017}",
  volume =       "313",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4",
  ISBN =         "3-030-36567-0 (print), 3-030-36568-9 (e-book)",
  ISBN-13 =      "978-3-030-36567-7 (print), 978-3-030-36568-4
                 (e-book)",
  ISSN =         "2194-1009 (print), 2194-1017 (electronic)",
  LCCN =         "????",
  MRclass =      "00B20, 11-06, 26-06, 33-06, 47-06, 49-06, 52-06,
                 62P05, 91G99, 97-06",
  bibdate =      "Tue Apr 21 10:22:01 MDT 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  series =       "Springer Proceedings in Mathematics \& Statistics",
  ZMnumber =     "07174492",
  acknowledgement = ack-nhfb,
  remark =       "Book.",
  subject =      "Education / Teaching Methods and Materials /
                 Mathematics; Mathematics / Applied; Mathematics /
                 Mathematical Analysis; Mathematics / Number Theory",
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  tableofcontents = "Part I: Applied Analysis, Optimisation, and
                 Convexity \\
                 Introduction / Regina S. Burachik and Guoyin Li / 3--5
                 \\
                 Symmetry and the Monotonicity of Certain Riemann Sums /
                 David Borwein and Jonathan M. Borwein and Brailey Sims
                 / 7--20 \\
                 Risk and Utility in the Duality Framework of Convex
                 Analysis / R. Tyrrell Rockafellar / 21--42 \\
                 Characterizations of Robust and Stable Duality for
                 Linearly Perturbed Uncertain Optimization Problems /
                 Nguyen Dinh and Miguel A. Goberna and Marco A. Lopez
                 and Michel Volle / 43--74 \\
                 Comparing Averaged Relaxed Cutters and Projection
                 Methods: Theory and Examples / Reinier Diaz Millan and
                 Scott B. Lindstrom and Vera Roshchina / 75--98 \\
                 Part II: Education \\
                 Introduction / Naomi Simone Borwein / 101--102 \\
                 On the Educational Legacies of Jonathan M. Borwein /
                 Naomi Simone Borwein and Judy-anne Heather Osborn /
                 103--131 \\
                 How Mathematicians Learned to Stop Worrying and Love
                 the Computer / Keith Devlin / 133--139 \\
                 Crossing Boundaries: Fostering Collaboration Between
                 Mathematics Educators and Mathematicians in Initial
                 Teacher Education Programmes / Merrilyn Goos / 141--148
                 \\
                 Mathematics Education in the Computational Age:
                 Challenges and Opportunities / Kathryn Holmes /
                 149--152 \\
                 Mathematics Education for Indigenous Students in
                 Preparation for Engineering and Information
                 Technologies / Collin Phillips and Fu Ken Ly / 153--169
                 \\
                 Origami as a Teaching Tool for Indigenous Mathematics
                 Education / Michael Assis and Michael Donovan /
                 171--188 \\
                 Dynamic Visual Models: Ancient Ideas and New
                 Technologies / Damir Jungic and Veselin Jungic /
                 189--201 \\
                 A Random Walk Through Experimental Mathematics / Eunice
                 Y. S. Chan and Robert M. Corless / 203--226 \\
                 Part III: Financial Mathematics \\
                 Introduction / David H. Bailey and Qiji J. Zhu /
                 229--231 \\
                 A Holistic Approach to Empirical Analysis: The
                 Insignificance of $P$, Hypothesis Testing and
                 Statistical Significance* / Morris Altman / 233--253
                 \\
                 Do Financial Gurus Produce Reliable Forecasts? / David
                 H. Bailey and Jonathan M. Borwein and Amir Salehipour
                 and Marcos Lopez de Prado / 255--274 \\
                 Entropy Maximization in Finance / Jonathan M. Borwein
                 and Qiji J. Zhu / 275--295 \\
                 Part IV: Number Theory, Special Functions, and Pi \\
                 Introduction / Richard P. Brent / 299--302 \\
                 Binary Constant-Length Substitutions and Mahler
                 Measures of Borwein Polynomials / Michael Baake and
                 Michael Coons and Neil Manibo / 303--322 \\
                 The Borwein Brothers, Pi and the AGM / Richard P. Brent
                 / 323--347 \\
                 The Road to Quantum Computational Supremacy / Cristian
                 S. Calude and Elena Calude / 349--367 \\
                 Nonlinear Identities for Bernoulli and Euler
                 Polynomials / Karl Dilcher / 369--376 \\
                 Metrical Theory for Small Linear Forms and Applications
                 to Interference Alignment / Mumtaz Hussain and Seyyed
                 Hassan Mahboubi and Abolfazl Seyed Motahari / 377--393
                 \\
                 Improved Bounds on Brun's Constant / Dave Platt and Tim
                 Trudgian / 395--406 \\
                 Extending the PSLQ Algorithm to Algebraic Integer
                 Relations / Matthew P. Skerritt and Paul Vrbik /
                 407--421 \\
                 Short Walk Adventures / Armin Straub and Wadim Zudilin
                 / 423--439",
}