# bibtab

bibtype: book
filename: elefunt.bib
label: Yoshida:1997:HFM
author: Masaaki Yoshida
title: Hypergeometric Functions, My Love: Modular Interpretations of Configuration Spaces
volume: E 32
publisher: pub-VIEWEG
address: pub-VIEWEG:adr
pages: xvi + 292
year: 1997
ISBN: 3-528-06925-2 OR 3528069252
ISBN13: 978-3-528-06925-4 OR 9783528069254
ISSN: 0179-2156 OR 01792156
LCCN: QA353.H9 Y67 1997
bibdate: Sat Oct 30 21:12:24 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 21:12:24 MDT
series: Aspects of mathematics
subject: Hypergeometric functions; Configuration space
acknowledgement: ack-nhfb
rawauthor: Masaaki Yoshida
rawtitle: Hypergeometric Functions, My Love: Modular Interpretations of Configuration Spaces
TOC:
Part 1: The Story of the Configuration Space $X(2,4)$ of Four Points on the Projective Line I. Configuration Spaces --- The Simplest Case II. Elliptic Curves III. Modular Interpretations of X(2,4) IV. Hypergeometric Integrals and Loaded Cycles 2 The Story of the Configuration Space X(2,n) of n Points on the Projective Line V. The Configuration Space X(2,5) VI. Modular Interpretation of the Configuration Space X(2,n) 3 The Story of the Configuration Space X(3,6) of Six Lines on the Projective Plane VII The Configuration Space X(3,6) VIII. Hypergeometric Functions of Type (3,6) IX. Modular Interpretation of the Configuration Space X(3,6)

rawTOC:
Part 1: The Story of the Configuration Space $X(2,4)$ of Four Points on the Projective Line \\ I. Configuration Spaces --- The Simplest Case \\ II. Elliptic Curves \\ III. Modular Interpretations of X(2,4) \\ IV. Hypergeometric Integrals and Loaded Cycles \\ 2 The Story of the Configuration Space X(2,n) of n Points on the Projective Line \\ V. The Configuration Space X(2,5) \\ VI. Modular Interpretation of the Configuration Space X(2,n) \\ 3 The Story of the Configuration Space X(3,6) of Six Lines on the Projective Plane \\ VII The Configuration Space X(3,6) \\ VIII. Hypergeometric Functions of Type (3,6) \\ IX. Modular Interpretation of the Configuration Space X(3,6)

entry:
@Book{Yoshida:1997:HFM,
  author =       "Masaaki Yoshida",
  title =        "Hypergeometric Functions, My Love: Modular
                 Interpretations of Configuration Spaces",
  volume =       "E 32",
  publisher =    pub-VIEWEG,
  address =      pub-VIEWEG:adr,
  pages =        "xvi + 292",
  year =         "1997",
  ISBN =         "3-528-06925-2",
  ISBN-13 =      "978-3-528-06925-4",
  ISSN =         "0179-2156",
  LCCN =         "QA353.H9 Y67 1997",
  bibdate =      "Sat Oct 30 21:12:24 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Aspects of mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions; Configuration space",
  tableofcontents = "Part 1: The Story of the Configuration Space
                 $X(2,4)$ of Four Points on the Projective Line \\
                 I. Configuration Spaces --- The Simplest Case \\
                 II. Elliptic Curves \\
                 III. Modular Interpretations of X(2,4) \\
                 IV. Hypergeometric Integrals and Loaded Cycles \\
                 2 The Story of the Configuration Space X(2,n) of n
                 Points on the Projective Line \\
                 V. The Configuration Space X(2,5) \\
                 VI. Modular Interpretation of the Configuration Space
                 X(2,n) \\
                 3 The Story of the Configuration Space X(3,6) of Six
                 Lines on the Projective Plane \\
                 VII The Configuration Space X(3,6) \\
                 VIII. Hypergeometric Functions of Type (3,6) \\
                 IX. Modular Interpretation of the Configuration Space
                 X(3,6)",
}


bibtype: article
filename: elefunt.bib
label: Yousif:1997:BFF
author: Hashim A. Yousif and Richard Melka
title: Bessel function of the first kind with complex argument
journal: j-COMP-PHYS-COMM
volume: 106
number: 3
pages: 199--206
month: nov
monthnumber: 11
year: 1997
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(97)00087-8
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:30:21 MST 2012
bibtimestamp: 2012.02.13 21:30:21 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465597000878
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Hashim A. Yousif and Richard Melka
rawtitle: {Bessel} function of the first kind with complex argument
abstract:
A new method of computing integral order Bessel functions of the first kind $ J_n(z) $ when either the absolute value of the real part or the imaginary part of the argument $ z = x + i y $ is small, is described. This method is based on computing the Bessel functions from asymptotic expressions when $ x sim 0 $ (or $ y sim 0 $ ). These expansions are derived from the integral definition of Bessel functions. This method is necessary because some existing algorithms and methods fail to give correct results for small $x$ or small $y$. In addition, our overall method of computing Bessel functions of any order and argument is discussed and the logarithmic derivative is used in computing these functions. The starting point of the backward recurrence relations needed to evaluate the Bessel function and their logarithmic derivatives are investigated in order to obtain accurate numerical results. Our numerical method, together with established techniques of computing the Bessel functions, is easy to implement, efficient, and produces reliable results for all $z$.

rawabstract:
A new method of computing integral order Bessel functions of the first kind $ J_n(z) $ when either the absolute value of the real part or the imaginary part of the argument $ z = x + i y $ is small, is described. This method is based on computing the Bessel functions from asymptotic expressions when $ x \sim 0 $ (or $ y \sim 0 $ ). These expansions are derived from the integral definition of Bessel functions. This method is necessary because some existing algorithms and methods fail to give correct results for small $x$ or small $y$. In addition, our overall method of computing Bessel functions of any order and argument is discussed and the logarithmic derivative is used in computing these functions. The starting point of the backward recurrence relations needed to evaluate the Bessel function and their logarithmic derivatives are investigated in order to obtain accurate numerical results. Our numerical method, together with established techniques of computing the Bessel functions, is easy to implement, efficient, and produces reliable results for all $z$.

entry:
@Article{Yousif:1997:BFF,
  author =       "Hashim A. Yousif and Richard Melka",
  title =        "{Bessel} function of the first kind with complex
                 argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "106",
  number =       "3",
  pages =        "199--206",
  month =        nov,
  year =         "1997",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(97)00087-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:21 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465597000878",
  abstract =     "A new method of computing integral order Bessel
                 functions of the first kind $ J_n(z) $ when either the
                 absolute value of the real part or the imaginary part
                 of the argument $ z = x + i y $ is small, is described.
                 This method is based on computing the Bessel functions
                 from asymptotic expressions when $ x \sim 0 $ (or $ y
                 \sim 0 $ ). These expansions are derived from the
                 integral definition of Bessel functions. This method is
                 necessary because some existing algorithms and methods
                 fail to give correct results for small $x$ or small
                 $y$. In addition, our overall method of computing
                 Bessel functions of any order and argument is discussed
                 and the logarithmic derivative is used in computing
                 these functions. The starting point of the backward
                 recurrence relations needed to evaluate the Bessel
                 function and their logarithmic derivatives are
                 investigated in order to obtain accurate numerical
                 results. Our numerical method, together with
                 established techniques of computing the Bessel
                 functions, is easy to implement, efficient, and
                 produces reliable results for all $z$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Zhang:1997:CSA
author: Jun Zhang and John A. Belward
title: Chebyshev series approximations for the Bessel function $ Y_n(z) $ of complex argument
journal: j-APPL-MATH-COMP
volume: 88
number: 2--3
pages: 275--286
day: 30
month: dec
monthnumber: 12
year: 1997
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/S0096-3003(96)00335-9
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Tue Nov 20 21:02:59 MST 2012
bibtimestamp: 2012.11.20 21:02:59 MST
URL: http://www.sciencedirect.com/science/article/pii/S0096300396003359
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: Jun Zhang and John A. Belward
rawtitle: {Chebyshev} series approximations for the {Bessel} function {$ Y_n(z) $} of complex argument
bibsource:
http://www.sciencedirect.com/science/journal/00963003; https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Zhang:1997:CSA,
  author =       "Jun Zhang and John A. Belward",
  title =        "{Chebyshev} series approximations for the {Bessel}
                 function {$ Y_n(z) $} of complex argument",
  journal =      j-APPL-MATH-COMP,
  volume =       "88",
  number =       "2--3",
  pages =        "275--286",
  day =          "30",
  month =        dec,
  year =         "1997",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/S0096-3003(96)00335-9",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:02:59 MST 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300396003359",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: Aberbour:1998:PMF
author: M. Aberbour and A. Houelle and H. Mehrez and N. Vaucher and A. Guyot
journal: j-IEEE-TRANS-VLSI-SYST
volume: 6
number: 1
pages: 114--121
month: mar
monthnumber: 3
year: 1998
CODEN: IEVSE9
DOI: https://doi.org/10.1109/92.661253
ISSN: 1063-8210 (print), 1557-9999 (electronic) OR 10638210 (print), 15579999 (electronic)
ISSNL: 1063-8210 OR 10638210
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Very Large Scale Integration (VLSI) Systems
acknowledgement: ack-nhfb
rawauthor: M. Aberbour and A. Houelle and H. Mehrez and N. Vaucher and A. Guyot
title:
On portable macrocell FPU generators for division and square root operators complying to the full IEEE-754 standard

rawtitle:
On portable macrocell {FPU} generators for division and square root operators complying to the full {IEEE-754} standard

entry:
@Article{Aberbour:1998:PMF,
  author =       "M. Aberbour and A. Houelle and H. Mehrez and N.
                 Vaucher and A. Guyot",
  title =        "On portable macrocell {FPU} generators for division
                 and square root operators complying to the full
                 {IEEE-754} standard",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "6",
  number =       "1",
  pages =        "114--121",
  month =        mar,
  year =         "1998",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/92.661253",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  summary =      "In this paper, we investigate the design of macrocell
                 generators of division and square root floating-point
                 operators. The number representation used in our
                 operators is the IEEE-754-1985 standard for binary
                 floating-point numbers. The design and \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Adamchik:1998:PFN
author: Victor S. Adamchik
title: Polygamma functions of negative order
journal: j-J-COMPUT-APPL-MATH
volume: 100
number: 2
pages: 191--199
day: 21
month: dec
monthnumber: 12
year: 1998
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:39:42 MST 2017
bibtimestamp: 2017.02.25 12:39:42 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042798001927
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Victor S. Adamchik
rawtitle: {Polygamma} functions of negative order
entry:
@Article{Adamchik:1998:PFN,
  author =       "Victor S. Adamchik",
  title =        "{Polygamma} functions of negative order",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "100",
  number =       "2",
  pages =        "191--199",
  day =          "21",
  month =        dec,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:39:42 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798001927",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Alzer:1998:CHM
author: Horst Alzer
journal: j-J-COMPUT-APPL-MATH
volume: 90
number: 2
pages: 265--265
day: 17
month: apr
monthnumber: 4
year: 1998
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(98)00040-5
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:08 MST 2017
bibtimestamp: 2017.02.25 12:36:08 MST
note: See cite Alzer:1997:HMI.
URL: http://www.sciencedirect.com/science/article/pii/S0377042798000405
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Horst Alzer
rawnote: See \cite{Alzer:1997:HMI}.
title:
Corrigendum: A harmonic mean inequality for the gamma function [J. Comput. Appl. Math. bf 87 (1997) 195--198]

rawtitle:
Corrigendum: {A harmonic mean inequality for the gamma function [J. Comput. Appl. Math. {\bf 87} (1997) 195--198]}

entry:
@Article{Alzer:1998:CHM,
  author =       "Horst Alzer",
  title =        "Corrigendum: {A harmonic mean inequality for the gamma
                 function [J. Comput. Appl. Math. {\bf 87} (1997)
                 195--198]}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "90",
  number =       "2",
  pages =        "265--265",
  day =          "17",
  month =        apr,
  year =         "1998",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(98)00040-5",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:08 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  note =         "See \cite{Alzer:1997:HMI}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798000405",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: book
filename: elefunt.bib
label: Andrews:1998:SFM
author: Larry C. Andrews
title: Special functions of mathematics for engineers
publisher: pub-OXFORD
address: pub-OXFORD:adr
edition: Second
pages: xvii + 479
year: 1998
LCCN: QA351 .A75 1998
bibdate: Sat Oct 30 16:44:00 MDT 2010
bibtimestamp: 2010.10.30 16:44:00 MDT
remark: Originally published: New York : McGraw-Hill, c1992.
subject: Functions, Special
acknowledgement: ack-nhfb
rawauthor: Larry C. Andrews
rawtitle: Special functions of mathematics for engineers
ISBN:
0-19-856558-5 (Oxford hardcover), 0-8194-2616-4 (SPIE Press hardcover) OR 0198565585 (Oxford hardcover), 0819426164 (SPIE Press hardcover)

ISBN13:
978-0-19-856558-1 (Oxford hardcover), 978-0-8194-2616-1 (SPIE Press) OR 9780198565581 (Oxford hardcover), 9780819426161 (SPIE Press)

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; library.ox.ac.uk:210/ADVANCE; z3950.loc.gov:7090/Voyager

TOC:
Preface to the Second Edition Preface to the First Edition Notation for Special Functions Infinite Series, Improper Integrals, and Infinite Products The Gamma Function and Related Functions Other Functions Defined by Integrals Legendre Polynomials and Related Functions Other Orthogonal Polynomials Bessel Functions Bessel Functions of Other Kinds Applications Involving Bessel Functions The Hypergeometric Function The Confluent Hypergeometric Functions Generalized Hypergeometric Functions Applications Involving Hypergeometric-Type Functions Bibliography Appendix: A List of Special Function Formulas Selected Answers to Exercises Index

rawTOC:
Preface to the Second Edition \\ Preface to the First Edition \\ Notation for Special Functions \\ Infinite Series, Improper Integrals, and Infinite Products \\ The Gamma Function and Related Functions \\ Other Functions Defined by Integrals \\ Legendre Polynomials and Related Functions \\ Other Orthogonal Polynomials \\ Bessel Functions \\ Bessel Functions of Other Kinds \\ Applications Involving Bessel Functions \\ The Hypergeometric Function \\ The Confluent Hypergeometric Functions \\ Generalized Hypergeometric Functions \\ Applications Involving Hypergeometric-Type Functions \\ Bibliography \\ Appendix: A List of Special Function Formulas \\ Selected Answers to Exercises \\ Index

entry:
@Book{Andrews:1998:SFM,
  author =       "Larry C. Andrews",
  title =        "Special functions of mathematics for engineers",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  edition =      "Second",
  pages =        "xvii + 479",
  year =         "1998",
  ISBN =         "0-19-856558-5 (Oxford hardcover), 0-8194-2616-4 (SPIE
                 Press hardcover)",
  ISBN-13 =      "978-0-19-856558-1 (Oxford hardcover),
                 978-0-8194-2616-1 (SPIE Press)",
  LCCN =         "QA351 .A75 1998",
  bibdate =      "Sat Oct 30 16:44:00 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 library.ox.ac.uk:210/ADVANCE;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Originally published: New York : McGraw-Hill, c1992.",
  subject =      "Functions, Special",
  tableofcontents = "Preface to the Second Edition \\
                 Preface to the First Edition \\
                 Notation for Special Functions \\
                 Infinite Series, Improper Integrals, and Infinite
                 Products \\
                 The Gamma Function and Related Functions \\
                 Other Functions Defined by Integrals \\
                 Legendre Polynomials and Related Functions \\
                 Other Orthogonal Polynomials \\
                 Bessel Functions \\
                 Bessel Functions of Other Kinds \\
                 Applications Involving Bessel Functions \\
                 The Hypergeometric Function \\
                 The Confluent Hypergeometric Functions \\
                 Generalized Hypergeometric Functions \\
                 Applications Involving Hypergeometric-Type Functions
                 \\
                 Bibliography \\
                 Appendix: A List of Special Function Formulas \\
                 Selected Answers to Exercises \\
                 Index",
}


bibtype: book
filename: elefunt.bib
label: Anonymous:1998:AMS
editor: Anonymous
title: Analytical methods and special functions
publisher: Gordon and Breach Science Publishers
address: Amsterdam, The Netherlands
year: 1998
ISSN: 1027-0264 OR 10270264
LCCN: A299.6 A533 v. 1 1998
bibdate: Sat Oct 30 19:02:18 2010
bibsource: http://cat.cisti-icist.nrc-cnrc.gc.ca/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:02:18 ???
acknowledgement: ack-nhfb
raweditor: Anonymous
rawtitle: Analytical methods and special functions
entry:
@Book{Anonymous:1998:AMS,
  editor =       "Anonymous",
  title =        "Analytical methods and special functions",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "Amsterdam, The Netherlands",
  pages =        "????",
  year =         "1998",
  ISSN =         "1027-0264",
  LCCN =         "A299.6 A533 v. 1 1998",
  bibdate =      "Sat Oct 30 19:02:18 2010",
  bibsource =    "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Antelo:1998:CVH
author: E. Antelo and T. Lang and J. D. Bruguera
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 2
pages: 152--161
month: feb
monthnumber: 2
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.663761
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:53 MDT 2011
bibtimestamp: 2011.07.06 09:35:53 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663761
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. Antelo and T. Lang and J. D. Bruguera
title:
Computation of $ sqrt (x / d) $ in a very high radix combined division / square-root unit with scaling and selection by rounding

rawtitle:
Computation of $ \sqrt {(x / d)} $ in a very high radix combined division\slash square-root unit with scaling and selection by rounding

entry:
@Article{Antelo:1998:CVH,
  author =       "E. Antelo and T. Lang and J. D. Bruguera",
  title =        "Computation of $ \sqrt {(x / d)} $ in a very high
                 radix combined division\slash square-root unit with
                 scaling and selection by rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "2",
  pages =        "152--161",
  month =        feb,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.663761",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:53 MDT 2011",
  bibsource =    "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/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663761",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A very-high radix digit-recurrence algorithm for the
                 operation {\surd}(x/d) is developed, with residual
                 scaling and digit selection by rounding. This is an
                 extension of the division and square-root algorithms
                 presented previously, and for which a \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: BenGhanem:1998:QFU
author: Riadh Ben Ghanem
title: Quadrature formulae using zeros of Bessel functions as nodes
journal: j-MATH-COMPUT
volume: 67
number: 221
pages: 323--336
month: jan
monthnumber: 1
year: 1998
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D32
MRnumber: 98c:65031
MRreviewer: Kai Diethelm
bibdate: Fri Jul 16 10:38:50 MDT 1999
bibsource: http://www.ams.org/mcom/1998-67-221; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.07.16 10:38:50 MDT
URL: http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00882-5&u=/mcom/1998-67-221/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Riadh {Ben Ghanem}
rawtitle: Quadrature formulae using zeros of {Bessel} functions as nodes
entry:
@Article{BenGhanem:1998:QFU,
  author =       "Riadh {Ben Ghanem}",
  title =        "Quadrature formulae using zeros of {Bessel} functions
                 as nodes",
  journal =      j-MATH-COMPUT,
  volume =       "67",
  number =       "221",
  pages =        "323--336",
  month =        jan,
  year =         "1998",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D32",
  MRnumber =     "98c:65031",
  MRreviewer =   "Kai Diethelm",
  bibdate =      "Fri Jul 16 10:38:50 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1998-67-221;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00882-5&u=/mcom/1998-67-221/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: techreport
filename: elefunt.bib
label: Borwein:1998:CSR
author: Jonathan M. Borwein and David M. Bradley and Richard E. Crandall
title: Computational Strategies for the Riemann Zeta Function
type: Report
number: CECM-98-118
institution: inst-CECM
address: inst-CECM:adr
pages: 68
day: 30
month: oct
monthnumber: 10
year: 1998
bibdate: Mon Oct 24 11:29:15 2011
bibtimestamp: 2011.10.24 11:29:15 ???
note: Published in cite Borwein:2000:CSR.
URL: http://docserver.carma.newcastle.edu.au/211; http://people.reed.edu/~crandall/papers/attach01.pdf
acknowledgement: ack-nhfb
rawauthor: Jonathan M. Borwein and David M. Bradley and Richard E. Crandall
rawnote: Published in \cite{Borwein:2000:CSR}.
rawtitle: Computational Strategies for the {Riemann} Zeta Function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
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/elefunt.bib

abstract:
We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the incidence of what we call ``value recycling.''

authordates:
Jonathan Michael Borwein (20 May 1951--2 August 2016); Richard Eugene Crandall (29 December 1947--20 December 2012)

rawabstract:
We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the incidence of what we call ``value recycling.''

entry:
@TechReport{Borwein:1998:CSR,
  author =       "Jonathan M. Borwein and David M. Bradley and Richard
                 E. Crandall",
  title =        "Computational Strategies for the {Riemann} Zeta
                 Function",
  type =         "Report",
  number =       "CECM-98-118",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "68",
  day =          "30",
  month =        oct,
  year =         "1998",
  bibdate =      "Mon Oct 24 11:29:15 2011",
  bibsource =    "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/elefunt.bib",
  note =         "Published in \cite{Borwein:2000:CSR}.",
  URL =          "http://docserver.carma.newcastle.edu.au/211;
                 http://people.reed.edu/~crandall/papers/attach01.pdf",
  abstract =     "We provide a compendium of evaluation methods for the
                 Riemann zeta function, presenting formulae ranging from
                 historical attempts to recently found convergent series
                 to curious oddities old and new. We concentrate
                 primarily on practical computational issues, such
                 issues depending on the domain of the argument, the
                 desired speed of computation, and the incidence of what
                 we call ``value recycling.''",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016);
                 Richard Eugene Crandall (29 December 1947--20 December
                 2012)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: elefunt.bib
label: Buhring:1998:ACG
author: Wolfgang Buhring and H. M. Srivastava
editor: Themistocles M. Rassias
booktitle: Approximation theory and applications
publisher: Hadronic Press
address: Palm Harbor, FL, USA
pages: 17--35
year: 1998
ISBN: 1-57485-041-5 OR 1574850415
ISBN13: 978-1-57485-041-3 OR 9781574850413
LCCN: QA297.5 .A685 1998
MRclass: 33C20; 41-06 (00B15)
MRnumber: MR1924838 (2003i:33006); MR1924835 (2003c:41003)
bibdate: Thu Dec 01 10:08:00 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 10:08:00 ???
URL: http://catalog.hathitrust.org/api/volumes/oclc/42786578.html
remark: The paper treats $_p + 1F_p(z)$ for $ z approx 1 $. Available as arxiv:math/0102032.
acknowledgement: ack-nhfb
bookpages: v + 193
rawauthor: Wolfgang B{\"u}hring and H. M. Srivastava
rawbooktitle: Approximation theory and applications
raweditor: Themistocles M. Rassias
title:
Analytic Continuation of the Generalized Hypergeometric Series Near Unit Argument with Emphasis on the Zero-Balanced Series

rawtitle:
Analytic Continuation of the Generalized Hypergeometric Series Near Unit Argument with Emphasis on the Zero-Balanced Series

entry:
@InCollection{Buhring:1998:ACG,
  author =       "Wolfgang B{\"u}hring and H. M. Srivastava",
  editor =       "Themistocles M. Rassias",
  booktitle =    "Approximation theory and applications",
  title =        "Analytic Continuation of the Generalized
                 Hypergeometric Series Near Unit Argument with Emphasis
                 on the Zero-Balanced Series",
  publisher =    "Hadronic Press",
  address =      "Palm Harbor, FL, USA",
  bookpages =    "v + 193",
  pages =        "17--35",
  year =         "1998",
  ISBN =         "1-57485-041-5",
  ISBN-13 =      "978-1-57485-041-3",
  LCCN =         "QA297.5 .A685 1998",
  MRclass =      "33C20; 41-06 (00B15)",
  MRnumber =     "MR1924838 (2003i:33006); MR1924835 (2003c:41003)",
  bibdate =      "Thu Dec 01 10:08:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://catalog.hathitrust.org/api/volumes/oclc/42786578.html",
  acknowledgement = ack-nhfb,
  remark =       "The paper treats $_{p + 1F}_p(z)$ for $ z \approx 1 $.
                 Available as arxiv:math/0102032.",
}


bibtype: article
filename: elefunt.bib
label: Carsky:1998:IGF
author: Petr Carsky and Martin Polasek
title: Incomplete Gamma $ F_m(x) $ Functions for Real Negative and Complex Arguments
journal: j-J-COMPUT-PHYS
volume: 143
number: 1
pages: 259--265
day: 10
month: jun
monthnumber: 6
year: 1998
CODEN: JCTPAH
DOI: https://doi.org/10.1006/jcph.1998.5975
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Jan 2 07:55:26 MST 2012
bibtimestamp: 2012.01.02 07:55:26 MST
URL: http://www.sciencedirect.com/science/article/pii/S0021999198959757
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Petr C{\'a}rsky and Martin Pol{\'a}sek
rawtitle: Incomplete Gamma {$ F_m(x) $} Functions for Real Negative and Complex Arguments
entry:
@Article{Carsky:1998:IGF,
  author =       "Petr C{\'a}rsky and Martin Pol{\'a}sek",
  title =        "Incomplete Gamma {$ F_m(x) $} Functions for Real
                 Negative and Complex Arguments",
  journal =      j-J-COMPUT-PHYS,
  volume =       "143",
  number =       "1",
  pages =        "259--265",
  day =          "10",
  month =        jun,
  year =         "1998",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1006/jcph.1998.5975",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:26 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021999198959757",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Cornea-Hasegan:1998:PIC
author: Marius Cornea-Hasegan
journal: j-INTEL-TECH-J
volume: Q2
number: Q2
pages: 11
year: 1998
ISSN: 1535-766X OR 1535766X
bibdate: Fri Jun 01 06:02:08 2001
bibtimestamp: 2001.06.01 06:02:08 ???
acknowledgement: ack-nhfb
rawauthor: Marius Cornea-Hasegan
title:
Proving the IEEE Correctness of Iterative Floating-Point Square Root, Divide, and Remainder Algorithms

URL:
http://developer.intel.com/technology/itj/q21998/articles/art_3.htm; http://developer.intel.com/technology/itj/q21998/pdf/ieee.pdf

rawtitle:
Proving the {IEEE} Correctness of Iterative Floating-Point Square Root, Divide, and Remainder Algorithms

entry:
@Article{Cornea-Hasegan:1998:PIC,
  author =       "Marius Cornea-Hasegan",
  title =        "Proving the {IEEE} Correctness of Iterative
                 Floating-Point Square Root, Divide, and Remainder
                 Algorithms",
  journal =      j-INTEL-TECH-J,
  volume =       "Q2",
  number =       "Q2",
  pages =        "11",
  year =         "1998",
  ISSN =         "1535-766X",
  bibdate =      "Fri Jun 01 06:02:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://developer.intel.com/technology/itj/q21998/articles/art_3.htm;
                 http://developer.intel.com/technology/itj/q21998/pdf/ieee.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Crenshaw:1998:ISR
author: Jack W. Crenshaw
title: Integer Square Roots
journal: j-EMBED-SYS-PROG
volume: 11
number: 2
pages: 15--32
month: feb
monthnumber: 2
year: 1998
CODEN: EYPRE4
ISSN: 1040-3272 OR 10403272
bibdate: Fri Nov 28 16:31:58 2003
bibtimestamp: 2003.11.28 16:31:58 ???
URL: http://www.embedded.com/98/9802fe2.htm
fjournal: Embedded Systems Programming
acknowledgement: ack-mfc
rawauthor: Jack W. Crenshaw
rawtitle: Integer Square Roots
entry:
@Article{Crenshaw:1998:ISR,
  author =       "Jack W. Crenshaw",
  title =        "Integer Square Roots",
  journal =      j-EMBED-SYS-PROG,
  volume =       "11",
  number =       "2",
  pages =        "15--32",
  month =        feb,
  year =         "1998",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Fri Nov 28 16:31:58 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.embedded.com/98/9802fe2.htm",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}


bibtype: article
filename: elefunt.bib
label: Dattoli:1998:GBF
author: G. Dattoli and A. Torre and S. Lorenzutta and G. Maino
title: Generalized Bessel functions and Kapteyn series
journal: j-COMPUT-MATH-APPL
volume: 35
number: 8
pages: 117--125
month: apr
monthnumber: 4
year: 1998
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:48 MST 2017
bibtimestamp: 2017.03.01 21:48:48 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122198000509
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: G. Dattoli and A. Torre and S. Lorenzutta and G. Maino
rawtitle: Generalized {Bessel} functions and {Kapteyn} series
entry:
@Article{Dattoli:1998:GBF,
  author =       "G. Dattoli and A. Torre and S. Lorenzutta and G.
                 Maino",
  title =        "Generalized {Bessel} functions and {Kapteyn} series",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "35",
  number =       "8",
  pages =        "117--125",
  month =        apr,
  year =         "1998",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122198000509",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Deleglise:1998:C
author: Marc Deleglise and Joel Rivat
title: Computing $ psi (x) $
journal: j-MATH-COMPUT
volume: 67
number: 224
pages: 1691--1696
month: oct
monthnumber: 10
year: 1998
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11Y35 (11N56)
MRnumber: 1 474 649
bibdate: Fri Jul 16 10:38:58 MDT 1999
bibsource: http://www.ams.org/mcom/1998-67-224; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.07.16 10:38:58 MDT
URL: http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00977-6&u=/mcom/1998-67-224/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Marc Del{\'e}glise and Jo{\"e}l Rivat
rawtitle: Computing $ \psi (x) $
entry:
@Article{Deleglise:1998:C,
  author =       "Marc Del{\'e}glise and Jo{\"e}l Rivat",
  title =        "Computing $ \psi (x) $",
  journal =      j-MATH-COMPUT,
  volume =       "67",
  number =       "224",
  pages =        "1691--1696",
  month =        oct,
  year =         "1998",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y35 (11N56)",
  MRnumber =     "1 474 649",
  bibdate =      "Fri Jul 16 10:38:58 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1998-67-224;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00977-6&u=/mcom/1998-67-224/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Fowler:1998:SRA
author: David Fowler and Eleanor Robson
title: Square Root Approximations in Old Babylonian Mathematics: YBC 7289 in Context
journal: j-HIST-MATH
volume: 25
number: 4
pages: 366--378
month: nov
monthnumber: 11
year: 1998
CODEN: HIMADS
ISSN: 0315-0860 (print), 1090-249X (electronic) OR 03150860 (print), 1090249X (electronic)
ISSNL: 0315-0860 OR 03150860
bibdate: Wed Jun 26 06:19:31 MDT 2013
bibtimestamp: 2013.06.26 06:19:31 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0315086098922091
fjournal: Historia Mathematica
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03150860
rawauthor: David Fowler and Eleanor Robson
rawtitle: Square Root Approximations in Old {Babylonian} Mathematics: {YBC 7289} in Context
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib

entry:
@Article{Fowler:1998:SRA,
  author =       "David Fowler and Eleanor Robson",
  title =        "Square Root Approximations in Old {Babylonian}
                 Mathematics: {YBC 7289} in Context",
  journal =      j-HIST-MATH,
  volume =       "25",
  number =       "4",
  pages =        "366--378",
  month =        nov,
  year =         "1998",
  CODEN =        "HIMADS",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:19:31 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086098922091",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gautschi:1998:IGF
author: Walter Gautschi
title: The incomplete gamma functions since Tricomi
crossref: Anonymous:1998:TIC
pages: 203--237
year: 1998
bibdate: Fri May 31 16:38:24 2024
bibtimestamp: 2024.05.31 16:38:24 ???
URL: https://web.archive.org/web/20070503103643/http://citeseer.ist.psu.edu/gautschi98incomplete.html
acknowledgement: ack-nhfb
rawauthor: Walter Gautschi
rawtitle: The incomplete gamma functions since {Tricomi}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InProceedings{Gautschi:1998:IGF,
  author =       "Walter Gautschi",
  title =        "The incomplete gamma functions since {Tricomi}",
  crossref =     "Anonymous:1998:TIC",
  pages =        "203--237",
  year =         "1998",
  bibdate =      "Fri May 31 16:38:24 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://web.archive.org/web/20070503103643/http://citeseer.ist.psu.edu/gautschi98incomplete.html",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Giordano:1998:UTG
author: C. Giordano and A. Laforgia and J. Pecaric
title: Unified treatment of Gautschi--Kershaw type inequalities for the gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 99
number: 1--2
pages: 167--175
day: 16
month: nov
monthnumber: 11
year: 1998
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:13 MST 2017
bibtimestamp: 2017.02.25 12:36:13 MST
URL: http://www.sciencedirect.com/science/article/pii/S037704279800154X
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: C. Giordano and A. Laforgia and J. Pecari{\'c}
rawtitle: Unified treatment of {Gautschi--Kershaw} type inequalities for the gamma function
entry:
@Article{Giordano:1998:UTG,
  author =       "C. Giordano and A. Laforgia and J. Pecari{\'c}",
  title =        "Unified treatment of {Gautschi--Kershaw} type
                 inequalities for the gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "99",
  number =       "1--2",
  pages =        "167--175",
  day =          "16",
  month =        nov,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:13 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704279800154X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Harris:1998:MAL
author: Frank E. Harris
title: More About the Leaky Aquifer Function
journal: j-IJQC
volume: 70
number: 4--5
pages: 623--626
year: 1998
CODEN: IJQCB2
DOI: https://doi.org/10.1002/(SICI)1097-461X(1998)70:4/5<623::AID-QUA8>3.0.CO%3B2-X
ISSN: 0020-7608 (print), 1097-461X (electronic) OR 00207608 (print), 1097461X (electronic)
ISSNL: 0020-7608 OR 00207608
bibdate: Tue Oct 4 06:59:18 MDT 2011
bibtimestamp: 2011.10.04 06:59:18 MDT
fjournal: International Journal of Quantum Chemistry
acknowledgement: ack-nhfb
ajournal: Int. J. Quantum Chem.
journalURL: http://www.interscience.wiley.com/jpages/0020-7608/
onlinedate: 7 Dec 1998
rawauthor: Frank E. Harris
rawtitle: More About the Leaky Aquifer Function
bibsource:
http://www3.interscience.wiley.com/journalfinder.html; https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ijqc.bib; https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib

URL:
http://www3.interscience.wiley.com/cgi-bin/abstract?ID=75040; http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=75040&PLACEBO=IE.pdf

entry:
@Article{Harris:1998:MAL,
  author =       "Frank E. Harris",
  title =        "More About the Leaky Aquifer Function",
  journal =      j-IJQC,
  volume =       "70",
  number =       "4--5",
  pages =        "623--626",
  month =        "????",
  year =         "1998",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/(SICI)1097-461X(1998)70:4/5<623::AID-QUA8>3.0.CO%3B2-X",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Tue Oct 4 06:59:18 MDT 2011",
  bibsource =    "http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=75040;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=75040&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Quantum Chem.",
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  onlinedate =   "7 Dec 1998",
}


bibtype: article
filename: elefunt.bib
label: Homeier:1998:AHC
author: Herbert H. H. Homeier
journal: j-NUMER-ALGORITHMS
volume: 18
number: 1
pages: 1--30
month: sep
monthnumber: 9
year: 1998
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Sep 29 08:36:54 MDT 2003
bibtimestamp: 2003.09.29 08:36:54 MDT
fjournal: Numerical Algorithms
keywords: convergence acceleration
ZMnumber: 914.65140
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Herbert H. H. Homeier
title:
An asymptotically hierarchy-consistent, iterative sequence transformation for convergence acceleration of Fourier series

bibsource:
http://www.kluweronline.com/issn/1017-1398; http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/fulltext.pdf; http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA972

rawtitle:
An asymptotically hierarchy-consistent, iterative sequence transformation for convergence acceleration of {Fourier} series

entry:
@Article{Homeier:1998:AHC,
  author =       "Herbert H. H. Homeier",
  title =        "An asymptotically hierarchy-consistent, iterative
                 sequence transformation for convergence acceleration of
                 {Fourier} series",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "18",
  number =       "1",
  pages =        "1--30",
  month =        sep,
  year =         "1998",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Sep 29 08:36:54 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/fulltext.pdf;
                 http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA972",
  ZMnumber =     "914.65140",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
  tech =         "Technical Report TC-NA-97-2, Institut f{\"u}r
                 {Physikalische} und {Theoretische Chemie,
                 Universit{\"a}t Regensburg, D-93040 Regensburg}, 1997",
}


bibtype: article
filename: elefunt.bib
label: Homeier:1998:CAM
author: H. H. H. Homeier
title: On Convergence Acceleration of Multipolar and Orthogonal Expansions
journal: j-INTERNET-J-CHEM
volume: 1
number: Article 28
year: 1998
CODEN: IJCHFJ
ISSN: 1099-8292 OR 10998292
note: Proceedings of the 4$^th$ Electronic Computational Chemistry Conference.
URL: http://www.ijc.com/articles/1998v1/28/
fjournal: Internet Journal of Chemistry
keywords: convergence acceleration
rawauthor: H. H. H. Homeier
rawnote: Proceedings of the {4$^{th}$ Electronic Computational Chemistry Conference}.
rawtitle: On Convergence Acceleration of Multipolar and Orthogonal Expansions
entry:
@Article{Homeier:1998:CAM,
  author =       "H. H. H. Homeier",
  title =        "On Convergence Acceleration of Multipolar and
                 Orthogonal Expansions",
  journal =      j-INTERNET-J-CHEM,
  volume =       "1",
  number =       "Article 28",
  pages =        "????",
  year =         "1998",
  CODEN =        "IJCHFJ",
  ISSN =         "1099-8292",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the {4$^{th}$ Electronic Computational
                 Chemistry Conference}.",
  URL =          "http://www.ijc.com/articles/1998v1/28/",
  fjournal =     "Internet Journal of Chemistry",
  keywords =     "convergence acceleration",
  tech =         "Technical Report TC-QM-97-5, Institut f{\"u}r
                 {Physikalische} und {Theoretische Chemie,
                 Universit{\"a}t Regensburg, D-93040 Regensburg}, 1997",
}


bibtype: article
filename: elefunt.bib
label: Jukic:1998:DTN
author: D. Jukic and T. Marossevic and R. Scitovski
title: Discrete total $ l_p $-norm approximation problem for the exponential function
journal: j-APPL-MATH-COMP
volume: 94
number: 2--3
pages: 137--143
day: 15
month: aug
monthnumber: 8
year: 1998
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/S0096-3003(97)10068-6
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Tue Nov 20 21:03:11 MST 2012
bibtimestamp: 2012.11.20 21:03:11 MST
URL: http://www.sciencedirect.com/science/article/pii/S0096300397100686
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: D. Juki{\'c} and T. Maros{\v{s}}evi{\'c} and R. Scitovski
rawtitle: Discrete total $ l_p $-norm approximation problem for the exponential function
bibsource:
http://www.sciencedirect.com/science/journal/00963003; https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Jukic:1998:DTN,
  author =       "D. Juki{\'c} and T. Maros{\v{s}}evi{\'c} and R.
                 Scitovski",
  title =        "Discrete total $ l_p $-norm approximation problem for
                 the exponential function",
  journal =      j-APPL-MATH-COMP,
  volume =       "94",
  number =       "2--3",
  pages =        "137--143",
  day =          "15",
  month =        aug,
  year =         "1998",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/S0096-3003(97)10068-6",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:03:11 MST 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300397100686",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: Kiranon:1998:SRV
author: W. Kiranon and N. Kumprasert
title: Square-rooting and vector summation circuits using current conveyors
volume: 145
number: 2
pages: 139
month: apr
monthnumber: 4
year: 1998
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
acknowledgement: ack-nhfb
rawauthor: W. Kiranon and N. Kumprasert
rawtitle: Square-rooting and vector summation circuits using current conveyors
journal:
IEE Proceedings on Circuits, Devices and Systems [see also IEE Proceedings G - Circuits, Devices and Systems]

entry:
@Article{Kiranon:1998:SRV,
  author =       "W. Kiranon and N. Kumprasert",
  title =        "Square-rooting and vector summation circuits using
                 current conveyors",
  journal =      "IEE Proceedings on Circuits, Devices and Systems [see
                 also IEE Proceedings G - Circuits, Devices and
                 Systems]",
  volume =       "145",
  number =       "2",
  pages =        "139",
  month =        apr,
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Recently, Lui [1995] presented a square-rooting
                 circuit using CCII, MOS transistors and a buffered
                 unity-gain inverting amplifier. It is interesting since
                 it finds various applications as described in his
                 paper. However, an error occurred in the \ldots{}",
}


bibtype: inbook
filename: elefunt.bib
label: Knuth:1998:EP
author: Donald E. Knuth
title: Evaluation of polynomials
crossref: Knuth:1998:SA
chapter: 4
pages: 485--524
year: 1998
bibdate: Fri Oct 20 11:29:58 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 11:29:58 ???
keywords: number of multiplications to evaluate a polynomial
acknowledgement: ack-nhfb
rawauthor: Donald E. Knuth
rawtitle: Evaluation of polynomials
remark:
This is the definitive treatment of the rearrangement of polynomial coefficients to reduce the multiplication count. See cite Todd:1955:MWN and references therein to early papers on the subject.

entry:
@InBook{Knuth:1998:EP,
  author =       "Donald E. Knuth",
  title =        "Evaluation of polynomials",
  crossref =     "Knuth:1998:SA",
  chapter =      "4",
  pages =        "485--524",
  year =         "1998",
  bibdate =      "Fri Oct 20 11:29:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "number of multiplications to evaluate a polynomial",
  remark =       "This is the definitive treatment of the rearrangement
                 of polynomial coefficients to reduce the multiplication
                 count. See \cite{Todd:1955:MWN} and references therein
                 to early papers on the subject.",
}


bibtype: article
filename: elefunt.bib
label: Kramer:1998:PWC
author: W. Kramer
title: A priori worst case error bounds for floating-point computations
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 7
pages: 750--756
month: jul
monthnumber: 7
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.709374
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:55 MDT 2011
bibtimestamp: 2011.07.06 09:35:55 MDT
note: See cite Tang:1992:TDI.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709374
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
authordates: 1952--2014 (WK)
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: W. Kramer
rawnote: See \cite{Tang:1992:TDI}.
rawtitle: A priori worst case error bounds for floating-point computations
abstract:
A new technique for the a priori calculation of rigorous error bounds for floating-point computations is introduced. The theorems given in the paper combined with interval arithmetic lead to the implementation of reliable software routines, which enable the user to compute the desired error bounds automatically by a suitable computer program. As a prominent example, a table-lookup algorithm for calculating the function $ e x p(x) - 1 $ that has been published by P. T. P. Tang (1992) is analyzed using these new tools. The result shows the high quality of the new approach

rawabstract:
A new technique for the a priori calculation of rigorous error bounds for floating-point computations is introduced. The theorems given in the paper combined with interval arithmetic lead to the implementation of reliable software routines, which enable the user to compute the desired error bounds automatically by a suitable computer program. As a prominent example, a table-lookup algorithm for calculating the function $ e x p(x) - 1 $ that has been published by P. T. P. Tang (1992) is analyzed using these new tools. The result shows the high quality of the new approach

entry:
@Article{Kramer:1998:PWC,
  author =       "W. Kramer",
  title =        "A priori worst case error bounds for floating-point
                 computations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "750--756",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.709374",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See \cite{Tang:1992:TDI}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709374",
  abstract =     "A new technique for the a priori calculation of
                 rigorous error bounds for floating-point computations
                 is introduced. The theorems given in the paper combined
                 with interval arithmetic lead to the implementation of
                 reliable software routines, which enable the user to
                 compute the desired error bounds automatically by a
                 suitable computer program. As a prominent example, a
                 table-lookup algorithm for calculating the function $ e
                 x p(x) - 1 $ that has been published by P. T. P. Tang
                 (1992) is analyzed using these new tools. The result
                 shows the high quality of the new approach",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  author-dates = "1952--2014 (WK)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Kravanja:1998:ZMS
author: P. Kravanja and O. Ragos and M. N. Vrahatis and F. A. Zafiropoulos
journal: j-COMP-PHYS-COMM
volume: 113
number: 2--3
pages: 220--238
month: oct
monthnumber: 10
year: 1998
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(98)00064-2
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:30:30 MST 2012
bibtimestamp: 2012.02.13 21:30:30 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465598000642
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: P. Kravanja and O. Ragos and M. N. Vrahatis and F. A. Zafiropoulos
title:
ZEBEC: a mathematical software package for computing simple zeros of Bessel functions of real order and complex argument

rawtitle:
{ZEBEC}: a mathematical software package for computing simple zeros of {Bessel} functions of real order and complex argument

entry:
@Article{Kravanja:1998:ZMS,
  author =       "P. Kravanja and O. Ragos and M. N. Vrahatis and F. A.
                 Zafiropoulos",
  title =        "{ZEBEC}: a mathematical software package for computing
                 simple zeros of {Bessel} functions of real order and
                 complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "113",
  number =       "2--3",
  pages =        "220--238",
  month =        oct,
  year =         "1998",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(98)00064-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:30 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465598000642",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: inproceedings
filename: elefunt.bib
label: Kuhlmann:1998:FLP
author: M. Kuhlmann and K. K. Parhi
title: Fast low-power shared division and square-root architecture
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 128--135
year: 1998
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: M. Kuhlmann and K. K. Parhi
rawtitle: Fast low-power shared division and square-root architecture
booktitle:
Proceedings of the 1998 International Conference on Computer Design: VLSI in Computers and Processors. ICCD '98

rawbooktitle:
{Proceedings of the 1998 International Conference on Computer Design: VLSI in Computers and Processors. ICCD '98}

entry:
@InProceedings{Kuhlmann:1998:FLP,
  author =       "M. Kuhlmann and K. K. Parhi",
  booktitle =    "{Proceedings of the 1998 International Conference on
                 Computer Design: VLSI in Computers and Processors. ICCD
                 '98}",
  title =        "Fast low-power shared division and square-root
                 architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "128--135",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper addresses a fast low-power implementation
                 of a shared division and square-root architecture. Two
                 approaches are considered in this paper; these include
                 the SRT (Sweeney, Robertson and Tocher) approach which
                 does not require prescaling and \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Lefevre:1998:TCR
author: V. Lefevre and J.-M. Muller and A. Tisserand
title: Toward correctly rounded transcendentals
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 11
pages: 1235--1243
month: nov
monthnumber: 11
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.736435
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: V. Lef{\`e}vre and J.-M. Muller and A. Tisserand
rawtitle: Toward correctly rounded transcendentals
entry:
@Article{Lefevre:1998:TCR,
  author =       "V. Lef{\`e}vre and J.-M. Muller and A. Tisserand",
  title =        "Toward correctly rounded transcendentals",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "11",
  pages =        "1235--1243",
  month =        nov,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.736435",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "The Table Maker's Dilemma is the problem of always
                 getting correctly rounded results when computing the
                 elementary functions. After a brief presentation of
                 this problem, we present new developments that have
                 helped us to solve this problem for the \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Lopez:1998:SSC
author: JoseL. Lopez
title: Several series containing gamma and polygamma functions
journal: j-J-COMPUT-APPL-MATH
volume: 90
number: 1
pages: 15--23
day: 6
month: apr
monthnumber: 4
year: 1998
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:07 MST 2017
bibtimestamp: 2017.02.25 12:36:07 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042798000077
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Jos{\'e}L. L{\'o}pez
rawtitle: Several series containing gamma and polygamma functions
entry:
@Article{Lopez:1998:SSC,
  author =       "Jos{\'e}L. L{\'o}pez",
  title =        "Several series containing gamma and polygamma
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "90",
  number =       "1",
  pages =        "15--23",
  day =          "6",
  month =        apr,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:07 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798000077",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Miller:1998:CGI
author: Allen R. Miller and Ira S. Moskowitz
title: On certain generalized incomplete gamma functions
journal: j-J-COMPUT-APPL-MATH
volume: 91
number: 2
pages: 179--190
day: 4
month: may
monthnumber: 5
year: 1998
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:08 MST 2017
bibtimestamp: 2017.02.25 12:36:08 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042798000314
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Allen R. Miller and Ira S. Moskowitz
rawtitle: On certain generalized incomplete gamma functions
entry:
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  number =       "2",
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  acknowledgement = ack-nhfb,
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bibtype: article
filename: elefunt.bib
label: Morozov:1998:NWR
author: D. Kh. Morozov and V. V. Voitsekhovich
title: A new wide-range approximation of modified Bessel functions in terms of elementary functions
journal: Rev. Mexicana Fi s.
volume: 44
number: 3
pages: 231--234
year: 1998
CODEN: RMXFAT
ISSN: 0035-001X OR 0035001X
MRclass: 65D20
MRnumber: MR1629601
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.13 06:46:35 ???
fjournal: Revista Mexicana de Fi sica
acknowledgement: ack-nhfb
rawauthor: D. Kh. Morozov and V. V. Voitsekhovich
rawtitle: A new wide-range approximation of modified {Bessel} functions in terms of elementary functions
entry:
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  author =       "D. Kh. Morozov and V. V. Voitsekhovich",
  title =        "A new wide-range approximation of modified {Bessel}
                 functions in terms of elementary functions",
  journal =      "Rev. Mexicana F\'\i s.",
  volume =       "44",
  number =       "3",
  pages =        "231--234",
  year =         "1998",
  CODEN =        "RMXFAT",
  ISSN =         "0035-001X",
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  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Revista Mexicana de F\'\i sica",
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bibtype: article
filename: elefunt.bib
label: Nguyen:1998:MLS
author: Phong Nguyen
title: A Montgomery-Like Square Root for the Number Field Sieve
journal: j-LECT-NOTES-COMP-SCI
volume: 1423
pages: 151--??
year: 1998
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Feb 5 11:52:18 MST 2002
bibtimestamp: 2002.02.05 11:52:18 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Phong Nguyen
rawtitle: A {Montgomery}-Like Square Root for the Number Field Sieve
bibsource:
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  author =       "Phong Nguyen",
  title =        "A {Montgomery}-Like Square Root for the Number Field
                 Sieve",
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  volume =       "1423",
  pages =        "151--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:52:18 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm;
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  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230151.htm;
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  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: elefunt.bib
label: Palumbo:1998:GSI
author: Biagio Palumbo
title: A generalization of some inequalities for the gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 88
number: 2
pages: 255--268
day: 2
month: mar
monthnumber: 3
year: 1998
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:06 MST 2017
bibtimestamp: 2017.02.25 12:36:06 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042797001878
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Biagio Palumbo
rawtitle: A generalization of some inequalities for the gamma function
entry:
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  author =       "Biagio Palumbo",
  title =        "A generalization of some inequalities for the gamma
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  volume =       "88",
  number =       "2",
  pages =        "255--268",
  day =          "2",
  month =        mar,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042797001878",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Qiu:1998:SIG
author: S.-L. Qiu and M. K. Vamanamurthy and M. Vuorinen
title: Some Inequalities for the Growth of Elliptic Integrals
journal: j-SIAM-J-MATH-ANA
volume: 29
number: 5
pages: 1224--1237
month: sep
monthnumber: 9
year: 1998
CODEN: SJMAAH
DOI: https://doi.org/10.1137/S0036141096310491
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
bibdate: Sat Dec 5 14:39:16 MST 1998
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SIMA/29/5; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.12.05 14:39:16 MST
URL: http://epubs.siam.org/sam-bin/dbq/article/31049
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: S.-L. Qiu and M. K. Vamanamurthy and M. Vuorinen
rawtitle: Some Inequalities for the Growth of Elliptic Integrals
entry:
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  author =       "S.-L. Qiu and M. K. Vamanamurthy and M. Vuorinen",
  title =        "Some Inequalities for the Growth of Elliptic
                 Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "29",
  number =       "5",
  pages =        "1224--1237",
  month =        sep,
  year =         "1998",
  CODEN =        "SJMAAH",
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  ISSN-L =       "0036-1410",
  bibdate =      "Sat Dec 5 14:39:16 MST 1998",
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  URL =          "http://epubs.siam.org/sam-bin/dbq/article/31049",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
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bibtype: article
filename: elefunt.bib
label: Rivolo:1998:CDR
author: M. T. Rivolo and A. Simi
journal: j-ARCH-HIST-EXACT-SCI
volume: 52
number: 2
pages: 161--193
month: feb
monthnumber: 2
year: 1998
CODEN: AHESAN
DOI: https://doi.org/10.1007/s004070050015
ISSN: 0003-9519 (print), 1432-0657 (electronic) OR 00039519 (print), 14320657 (electronic)
ISSNL: 0003-9519 OR 00039519
MRclass: 01A35 (01A40)
MRnumber: 1610136 (99d:01015)
MRreviewer: Massimo Galuzzi
bibdate: Fri Feb 4 21:50:33 MST 2011
bibtimestamp: 2011.02.04 21:50:33 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=52&issue=2&spage=161
fjournal: Archive for History of Exact Sciences
language: Italian
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/407
rawauthor: M. T. Rivolo and A. Simi
title:
Il Calcolo delle Radici Quadrate e Cubiche in Italia da Fibonacci a Bombelli. (Italian) [The calculation of square and cube roots in Italy from Fibonacci to Bombelli]

bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=52&issue=2; https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Il Calcolo delle Radici Quadrate e Cubiche in {Italia} da {Fibonacci} a {Bombelli}. ({Italian}) [{The} calculation of square and cube roots in {Italy} from {Fibonacci} to {Bombelli}]

entry:
@Article{Rivolo:1998:CDR,
  author =       "M. T. Rivolo and A. Simi",
  title =        "Il Calcolo delle Radici Quadrate e Cubiche in {Italia}
                 da {Fibonacci} a {Bombelli}. ({Italian}) [{The}
                 calculation of square and cube roots in {Italy} from
                 {Fibonacci} to {Bombelli}]",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "52",
  number =       "2",
  pages =        "161--193",
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  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=52&issue=2;
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  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=52&issue=2&spage=161",
  acknowledgement = ack-nhfb,
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bibtype: article
filename: elefunt.bib
label: Russinoff:1998:MCP
author: David M. Russinoff
journal: j-LMS-J-COMPUT-MATH
volume: 1
pages: 148--200
year: 1998
DOI: https://doi.org/10.1112/S1461157000000176
ISSN: 1461-1570 OR 14611570
ISSNL: 1461-1570 OR 14611570
MRclass: 68M07 (65Y99 68T15)
MRnumber: 99m:68015
MRreviewer: J. Michel Muller
bibdate: Fri Nov 29 08:13:48 2002
bibtimestamp: 2002.11.29 08:13:48 ???
URL: http://www.lms.ac.uk/jcm/1/lms1998-001/
fjournal: LMS Journal of Computation and Mathematics
acknowledgement: ack-nhfb
ajournal: LMS J. Comput. Math.
journalURL: http://journals.cambridge.org/action/displayJournal?jid=JCM
onlinedate: 01 February 2010
rawauthor: David M. Russinoff
title:
A Mechanically Checked Proof of IEEE Compliance of the Floating Point Multiplication, Division and Square Root Algorithms of the AMD-K7 Processor

bibsource:
http://journals.cambridge.org/action/displayJournal?jid=JCM; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib

note:
Appendices A and B available to subscribers electronically (http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)

rawnote:
Appendices A and B available to subscribers electronically (http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)

rawtitle:
A Mechanically Checked Proof of {IEEE} Compliance of the Floating Point Multiplication, Division and Square Root Algorithms of the {AMD-K7} Processor

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  author =       "David M. Russinoff",
  title =        "A Mechanically Checked Proof of {IEEE} Compliance of
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  journal =      j-LMS-J-COMPUT-MATH,
  volume =       "1",
  pages =        "148--200",
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  CODEN =        "????",
  DOI =          "https://doi.org/10.1112/S1461157000000176",
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  bibdate =      "Fri Nov 29 08:13:48 2002",
  bibsource =    "http://journals.cambridge.org/action/displayJournal?jid=JCM;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib",
  note =         "Appendices A and B available to subscribers
                 electronically
                 (http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and
                 http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)",
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  acknowledgement = ack-nhfb,
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  fjournal =     "LMS Journal of Computation and Mathematics",
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bibtype: article
filename: elefunt.bib
label: Segura:1998:PCF
author: J. Segura and A. Gil
title: Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments
journal: j-COMP-PHYS-COMM
volume: 115
number: 1
pages: 69--86
day: 1
month: dec
monthnumber: 12
year: 1998
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(98)00097-6
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:30:32 MST 2012
bibtimestamp: 2012.02.13 21:30:32 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465598000976
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: J. Segura and A. Gil
rawtitle: Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments
entry:
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  author =       "J. Segura and A. Gil",
  title =        "Parabolic cylinder functions of integer and
                 half-integer orders for nonnegative arguments",
  journal =      j-COMP-PHYS-COMM,
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  number =       "1",
  pages =        "69--86",
  day =          "1",
  month =        dec,
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  bibdate =      "Mon Feb 13 21:30:32 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
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  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465598000976",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
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bibtype: article
filename: elefunt.bib
label: Sidi:1998:UBC
author: Avram Sidi and Yair Shapira
title: Upper bounds for convergence rates of acceleration methods with initial iterations
journal: j-NUMER-ALGORITHMS
volume: 18
number: 2
pages: 113--132
month: sep
monthnumber: 9
year: 1998
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Sep 29 08:36:55 MDT 2003
bibtimestamp: 2003.09.29 08:36:55 MDT
fjournal: Numerical Algorithms
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Avram Sidi and Yair Shapira
rawtitle: Upper bounds for convergence rates of acceleration methods with initial iterations
bibsource:
http://www.kluweronline.com/issn/1017-1398; http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://ipsapp007.kluweronline.com/content/getfile/5058/14/1/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/14/1/fulltext.pdf

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  author =       "Avram Sidi and Yair Shapira",
  title =        "Upper bounds for convergence rates of acceleration
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  journal =      j-NUMER-ALGORITHMS,
  volume =       "18",
  number =       "2",
  pages =        "113--132",
  month =        sep,
  year =         "1998",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Sep 29 08:36:55 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 http://www.math.psu.edu/dna/contents/na.html;
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  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/14/1/abstract.htm;
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  fjournal =     "Numerical Algorithms",
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bibtype: article
filename: elefunt.bib
label: Wei:1998:NFS
author: Liqiang Wei
title: New formula for $9$--$j$ symbols and their direct calculation
journal: j-COMPUT-PHYS
volume: 12
number: 6
pages: 632--??
month: nov
monthnumber: 11
year: 1998
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.168745
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:46:17 MDT 2019
bibtimestamp: 2019.04.10 08:46:17 MDT
URL: https://aip.scitation.org/doi/10.1063/1.168745
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: Liqiang Wei
rawtitle: New formula for $9$--$j$ symbols and their direct calculation
entry:
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  author =       "Liqiang Wei",
  title =        "New formula for $9$--$j$ symbols and their direct
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  journal =      j-COMPUT-PHYS,
  volume =       "12",
  number =       "6",
  pages =        "632--??",
  month =        nov,
  year =         "1998",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168745",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:46:17 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168745",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
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bibtype: inproceedings
filename: elefunt.bib
label: Agarwal:1999:SAM
author: R. C. Agarwal and F. G. Gustavson and M. S. Schmookler
title: Series approximation methods for divide and square root in the Power3TM processor
crossref: Koren:1999:ISC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 116--123
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
keywords: ARITH; computer arithmetic; IEEE
acknowledgement: ack-nhfb
rawauthor: R. C. Agarwal and F. G. Gustavson and M. S. Schmookler
rawtitle: Series approximation methods for divide and square root in the {Power3{\TM}} processor
URL:
http://euler.ecs.umass.edu/paper/final/paper-144.pdf; http://euler.ecs.umass.edu/paper/final/paper-144.ps

entry:
@InProceedings{Agarwal:1999:SAM,
  author =       "R. C. Agarwal and F. G. Gustavson and M. S.
                 Schmookler",
  title =        "Series approximation methods for divide and square
                 root in the {Power3{\TM}} processor",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "116--123",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-144.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-144.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
  summary =      "The Power3 processor is a 64-bit implementation of the
                 PowerPC TM architecture and is the successor to the
                 Power2 TM processor for workstations and servers which
                 REQUIRE high performance floating point capability. The
                 previous \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Alzer:1999:SPP
author: Horst Alzer and O. G. Ruehr
title: A submultiplicative property of the psi function
journal: j-J-COMPUT-APPL-MATH
volume: 101
number: 1--2
pages: 53--60
day: 15
month: jan
monthnumber: 1
year: 1999
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:39:42 MST 2017
bibtimestamp: 2017.02.25 12:39:42 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042798001903
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Horst Alzer and O. G. Ruehr
rawtitle: A submultiplicative property of the psi function
entry:
@Article{Alzer:1999:SPP,
  author =       "Horst Alzer and O. G. Ruehr",
  title =        "A submultiplicative property of the psi function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "101",
  number =       "1--2",
  pages =        "53--60",
  day =          "15",
  month =        jan,
  year =         "1999",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:39:42 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798001903",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: book
filename: elefunt.bib
label: Andrews:1999:SF
author: George E. Andrews and Richard Askey and Ranjan Roy
title: Special Functions
volume: 71
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: xvi + 664
year: 1999
DOI: https://doi.org/10.1017/CBO9781107325937
LCCN: QA351 .A74 1999
bibdate: Mon Sep 17 18:52:30 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2001.09.17 18:52:30 ???
series: Encyclopedia of mathematics and its applications
subject: Functions, Special
acknowledgement: ack-nhfb
rawauthor: George E. Andrews and Richard Askey and Ranjan Roy
rawtitle: Special Functions
ISBN:
0-521-62321-9 (hardcover), 0-521-78988-5 (paperback), 1-107-32593-5 (e-book) OR 0521623219 (hardcover), 0521789885 (paperback), 1107325935 (ebook)

ISBN13:
978-0-521-62321-6 (hardcover), 978-0-521-78988-2 (paperback), 978-1-107-32593-7 (e-book) OR 9780521623216 (hardcover), 9780521789882 (paperback), 9781107325937 (ebook)

TOC:
Frontmatter / i--vi Contents / vii--xii Preface / xiii--xvi 1: The Gamma and Beta Functions / 1--60 2: The Hypergeometric Functions / 61--123 3: Hypergeometric Transformations and Identities / 124--186 4: Bessel Functions and Confluent Hypergeometric Functions / 187--239 5: Orthogonal Polynomials / 240--276 6: Special Orthogonal Polynomials / 277--354 7: Topics in Orthogonal Polynomials / 355--400 8: The Selberg Integral and Its Applications / 401--444 9: Spherical Harmonics / 445--480 10: Introduction to $q$-Series / 481--552 11: Partitions / 553--576 12: Bailey Chains / 577--594 A: Infinite Products / 595--598 B: Summability and Fractional Integration / 599--610 C: Asymptotic Expansions / 611--616 D: Euler--Maclaurin Summation Formula / 617--628 E: Lagrange Inversion Formula / 629--636 F: Series Solutions of Differential Equations / 637--640 Bibliography / 641--654 Index / 655--658 Subject Index / 659--662 Symbol Index / 663--664

rawTOC:
Frontmatter / i--vi \\ Contents / vii--xii \\ Preface / xiii--xvi \\ 1: The Gamma and Beta Functions / 1--60 \\ 2: The Hypergeometric Functions / 61--123 \\ 3: Hypergeometric Transformations and Identities / 124--186 \\ 4: Bessel Functions and Confluent Hypergeometric Functions / 187--239 \\ 5: Orthogonal Polynomials / 240--276 \\ 6: Special Orthogonal Polynomials / 277--354 \\ 7: Topics in Orthogonal Polynomials / 355--400 \\ 8: The Selberg Integral and Its Applications / 401--444 \\ 9: Spherical Harmonics / 445--480 \\ 10: Introduction to $q$-Series / 481--552 \\ 11: Partitions / 553--576 \\ 12: Bailey Chains / 577--594 \\ A: Infinite Products / 595--598 \\ B: Summability and Fractional Integration / 599--610 \\ C: Asymptotic Expansions / 611--616 \\ D: Euler--Maclaurin Summation Formula / 617--628 \\ E: Lagrange Inversion Formula / 629--636 \\ F: Series Solutions of Differential Equations / 637--640 \\ Bibliography / 641--654 \\ Index / 655--658 \\ Subject Index / 659--662 \\ Symbol Index / 663--664

entry:
@Book{Andrews:1999:SF,
  author =       "George E. Andrews and Richard Askey and Ranjan Roy",
  title =        "Special Functions",
  volume =       "71",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xvi + 664",
  year =         "1999",
  DOI =          "https://doi.org/10.1017/CBO9781107325937",
  ISBN =         "0-521-62321-9 (hardcover), 0-521-78988-5 (paperback),
                 1-107-32593-5 (e-book)",
  ISBN-13 =      "978-0-521-62321-6 (hardcover), 978-0-521-78988-2
                 (paperback), 978-1-107-32593-7 (e-book)",
  LCCN =         "QA351 .A74 1999",
  bibdate =      "Mon Sep 17 18:52:30 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$90.00 (hardcover), US\$34.95 (paperback)",
  series =       "Encyclopedia of mathematics and its applications",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special",
  tableofcontents = "Frontmatter / i--vi \\
                 Contents / vii--xii \\
                 Preface / xiii--xvi \\
                 1: The Gamma and Beta Functions / 1--60 \\
                 2: The Hypergeometric Functions / 61--123 \\
                 3: Hypergeometric Transformations and Identities /
                 124--186 \\
                 4: Bessel Functions and Confluent Hypergeometric
                 Functions / 187--239 \\
                 5: Orthogonal Polynomials / 240--276 \\
                 6: Special Orthogonal Polynomials / 277--354 \\
                 7: Topics in Orthogonal Polynomials / 355--400 \\
                 8: The Selberg Integral and Its Applications / 401--444
                 \\
                 9: Spherical Harmonics / 445--480 \\
                 10: Introduction to $q$-Series / 481--552 \\
                 11: Partitions / 553--576 \\
                 12: Bailey Chains / 577--594 \\
                 A: Infinite Products / 595--598 \\
                 B: Summability and Fractional Integration / 599--610
                 \\
                 C: Asymptotic Expansions / 611--616 \\
                 D: Euler--Maclaurin Summation Formula / 617--628 \\
                 E: Lagrange Inversion Formula / 629--636 \\
                 F: Series Solutions of Differential Equations /
                 637--640 \\
                 Bibliography / 641--654 \\
                 Index / 655--658 \\
                 Subject Index / 659--662 \\
                 Symbol Index / 663--664",
  xxURL =        "http://www.loc.gov/catdir/toc/cam024/98025757.html;
                 http://www.loc.gov/catdir/description/cam029/98025757.html",
}


bibtype: article
filename: elefunt.bib
label: Bach:1999:NTS
author: E. Bach and K. Huber
title: Note on taking square-roots modulo $N$
journal: j-IEEE-TRANS-INF-THEORY
volume: 45
number: 2
pages: 807--809
month: mar
monthnumber: 3
year: 1999
CODEN: IETTAW
DOI: https://doi.org/10.1109/18.749034
ISSN: 0018-9448 (print), 1557-9654 (electronic) OR 00189448 (print), 15579654 (electronic)
ISSNL: 0018-9448 OR 00189448
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Information Theory
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18
rawauthor: E. Bach and K. Huber
rawtitle: Note on taking square-roots modulo {$N$}
entry:
@Article{Bach:1999:NTS,
  author =       "E. Bach and K. Huber",
  title =        "Note on taking square-roots modulo {$N$}",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "45",
  number =       "2",
  pages =        "807--809",
  month =        mar,
  year =         "1999",
  CODEN =        "IETTAW",
  DOI =          "https://doi.org/10.1109/18.749034",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
  summary =      "In this article it is shown how Gauss' (1981) famous
                 cyclotomic sum formula can be used for extracting
                 square-roots modulo \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Batten:1999:IBO
author: D. Batten and S. Jinturkar and J. Glossner and M. Schulte and R. Peri and P. D'arcy
title: Interactions Between Optimizations and a New Type of DSP Intrinsic Function
pages: 807--809
year: 1999
bibdate: Sun Mar 04 11:05:23 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.03.04 11:05:23 ???
note: Shortened version in cite Batten:1999:IFB.
URL: http://mesa.ece.wisc.edu/publications/cp_1999-09.pdf
acknowledgement: ack-nhfb
rawauthor: D. Batten and S. Jinturkar and J. Glossner and M. Schulte and R. Peri and P. D'arcy
rawnote: Shortened version in \cite{Batten:1999:IFB}.
rawtitle: Interactions Between Optimizations and a New Type of {DSP} Intrinsic Function
booktitle:
Proceedings of the International Conference on Signal Processing Applications and Technologies, Orlando, Florida, November, 1999

rawbooktitle:
Proceedings of the International Conference on Signal Processing Applications and Technologies, Orlando, Florida, November, 1999

entry:
@InProceedings{Batten:1999:IBO,
  author =       "D. Batten and S. Jinturkar and J. Glossner and M.
                 Schulte and R. Peri and P. D'arcy",
  editor =       "????",
  booktitle =    "Proceedings of the International Conference on Signal
                 Processing Applications and Technologies, Orlando,
                 Florida, November, 1999",
  title =        "Interactions Between Optimizations and a New Type of
                 {DSP} Intrinsic Function",
  publisher =    "????",
  address =      "????",
  year =         "1999",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 04 11:05:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Shortened version in \cite{Batten:1999:IFB}.",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-09.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Batten:1999:IFB
author: D. Batten and P. D'arcy
title: Intrinsic Functions Boost Compilers
journal: Electrical Engineering Times
volume: 1085
pages: 104--104
month: nov
monthnumber: 11
year: 1999
bibdate: Sun Mar 04 11:06:22 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.03.04 11:06:22 ???
acknowledgement: ack-nhfb
rawauthor: D. Batten and P. D'arcy
rawtitle: Intrinsic Functions Boost Compilers
entry:
@Article{Batten:1999:IFB,
  author =       "D. Batten and P. D'arcy",
  title =        "Intrinsic Functions Boost Compilers",
  journal =      "Electrical Engineering Times",
  volume =       "1085",
  pages =        "104--104",
  month =        nov,
  year =         "1999",
  bibdate =      "Sun Mar 04 11:06:22 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: elefunt.bib
label: Beebe:1999:FAE
author: Nelson H. F. Beebe
title: Fast Approximate Exponential Functions
type: Report
institution: inst-CSC
address: inst-CSC:adr
pages: 104--104
day: 7
month: dec
monthnumber: 12
year: 1999
bibdate: Sat Feb 02 15:08:59 2019
bibtimestamp: 2019.02.02 15:08:59 ???
acknowledgement: ack-nhfb
rawauthor: Nelson H. F. Beebe
rawtitle: Fast Approximate Exponential Functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
This package contains software conforming to 1989 ANSI/ISO Standard C (ANSI X3.159-1989, ISO/IEC 9899-1990) and 1998 ISO Standard C++ (ISO/IEC 14882:1998) for testing an interesting algorithm for fast approximate exp() functions, published in cite Schraudolph:1999:FCA. There is a font error in figure 2 of that paper: all carets should be replaced by underscore.

remark:
From the report: ``Schraudolph's formula for the approximate exponential function computes $ a times x + b - c $ in floating-point arithmetic, then converts it to a 32-bit integer which is stored in the appropriate integer word overlaying the floating-point representation. The entire cost is thus a floating-point multiply and add (one instruction on some RISC architectures), a conversion to an integer, and a storage to memory.''

rawabstract:
This package contains software conforming to 1989 ANSI/ISO Standard C (ANSI X3.159-1989, ISO/IEC 9899-1990) and 1998 ISO Standard C++ (ISO/IEC 14882:1998) for testing an interesting algorithm for fast approximate exp() functions, published in \cite{Schraudolph:1999:FCA}. There is a font error in figure 2 of that paper: all carets should be replaced by underscore.

entry:
@TechReport{Beebe:1999:FAE,
  author =       "Nelson H. F. Beebe",
  title =        "Fast Approximate Exponential Functions",
  type =         "Report",
  institution =  inst-CSC,
  address =      inst-CSC:adr,
  day =          "7",
  month =        dec,
  year =         "1999",
  bibdate =      "Sat Feb 02 15:08:59 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This package contains software conforming to 1989
                 ANSI/ISO Standard C (ANSI X3.159-1989, ISO/IEC
                 9899-1990) and 1998 ISO Standard C++ (ISO/IEC
                 14882:1998) for testing an interesting algorithm for
                 fast approximate exp() functions, published in
                 \cite{Schraudolph:1999:FCA}. There is a font error in
                 figure 2 of that paper: all carets should be replaced
                 by underscore.",
  acknowledgement = ack-nhfb,
  remark =       "From the report: ``Schraudolph's formula for the
                 approximate exponential function computes $ a \times x
                 + b - c $ in floating-point arithmetic, then converts
                 it to a 32-bit integer which is stored in the
                 appropriate integer word overlaying the floating-point
                 representation. The entire cost is thus a
                 floating-point multiply and add (one instruction on
                 some RISC architectures), a conversion to an integer,
                 and a storage to memory.''",
}


bibtype: incollection
filename: elefunt.bib
label: Brezinski:1999:EEC
author: C. Brezinski
booktitle: Error control and adaptivity in scientific computing (Antalya, 1998)
title: Error estimates and convergence acceleration
volume: 536
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: 87--94
year: 1999
MRclass: 65B05 (65D15)
MRnumber: 1735125
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
series: NATO Sci. Ser. C Math. Phys. Sci.
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: C. Brezinski
rawbooktitle: Error control and adaptivity in scientific computing ({Antalya}, 1998)
rawtitle: Error estimates and convergence acceleration
entry:
@InCollection{Brezinski:1999:EEC,
  author =       "C. Brezinski",
  booktitle =    "Error control and adaptivity in scientific computing
                 ({Antalya}, 1998)",
  title =        "Error estimates and convergence acceleration",
  volume =       "536",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "87--94",
  year =         "1999",
  MRclass =      "65B05 (65D15)",
  MRnumber =     "1735125",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "NATO Sci. Ser. C Math. Phys. Sci.",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}


bibtype: inproceedings
filename: elefunt.bib
label: Bui:1999:DSI
author: H. Bui and S. Tahar
booktitle: 1999 IEEE Canadian Conference on Electrical and Computer Engineering, 9--12 May 1999
title: Design and synthesis of an IEEE-754 exponential function
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 450--455
year: 1999
bibdate: Sat Jul 16 17:14:11 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 17:14:11 MDT
acknowledgement: ack-nhfb
rawauthor: H. Bui and S. Tahar
rawbooktitle: 1999 {IEEE} Canadian Conference on Electrical and Computer Engineering, 9--12 May 1999
rawtitle: Design and synthesis of an {IEEE-754} exponential function
entry:
@InProceedings{Bui:1999:DSI,
  author =       "H. Bui and S. Tahar",
  booktitle =    "1999 {IEEE} Canadian Conference on Electrical and
                 Computer Engineering, 9--12 May 1999",
  title =        "Design and synthesis of an {IEEE-754} exponential
                 function",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "450--455",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 17:14:11 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We have designed a floating-point exponential function
                 using the table-driven method. The algorithm was first
                 implemented using sequential VHDL and later translated
                 to Concurrent Verilog. The main part of the work
                 consisted of creating modules that \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Cappuccino:1999:HSS
author: G. Cappuccino and G. Cocorullo and P. Corsonello and S. Perri
title: High speed self-timed pipelined datapath for square rooting
volume: 146
number: 1
pages: 16--22
month: feb
monthnumber: 2
year: 1999
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
acknowledgement: ack-nhfb
rawauthor: G. Cappuccino and G. Cocorullo and P. Corsonello and S. Perri
rawtitle: High speed self-timed pipelined datapath for square rooting
journal:
IEE Proceedings on Circuits, Devices and Systems [see also IEE Proceedings G --- Circuits, Devices and Systems]

entry:
@Article{Cappuccino:1999:HSS,
  author =       "G. Cappuccino and G. Cocorullo and P. Corsonello and
                 S. Perri",
  title =        "High speed self-timed pipelined datapath for square
                 rooting",
  journal =      "IEE Proceedings on Circuits, Devices and Systems [see
                 also IEE Proceedings G --- Circuits, Devices and
                 Systems]",
  volume =       "146",
  number =       "1",
  pages =        "16--22",
  month =        feb,
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The authors describe a new high-performance self-timed
                 circuit for asynchronous square rooting. The new
                 architecture is based on a modified nonrestoring
                 algorithm. An asynchronous pipelined cellular array
                 without auxiliary system for the \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1999:TSI
author: B. C. Carlson
title: Toward Symbolic Integration of Elliptic Integrals
journal: j-J-SYMBOLIC-COMP
volume: 28
number: 6
pages: 739--753
month: dec
monthnumber: 12
year: 1999
CODEN: JSYCEH
DOI: https://doi.org/10.1006/jsco.1999.0336
ISSN: 0747-7171 (print), 1095-855X (electronic) OR 07477171 (print), 1095855X (electronic)
ISSNL: 0747-7171 OR 07477171
bibdate: Tue Mar 7 11:48:04 MST 2000
bibsource: http://www.idealibrary.com/cgi-bin/links/toc/sy; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2000.03.07 11:48:04 MST
fjournal: Journal of Symbolic Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/07477171
rawauthor: B. C. Carlson
rawtitle: Toward Symbolic Integration of Elliptic Integrals
URL:
http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production; http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/pdf; http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/ref

entry:
@Article{Carlson:1999:TSI,
  author =       "B. C. Carlson",
  title =        "Toward Symbolic Integration of Elliptic Integrals",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "28",
  number =       "6",
  pages =        "739--753",
  month =        dec,
  year =         "1999",
  CODEN =        "JSYCEH",
  DOI =          "https://doi.org/10.1006/jsco.1999.0336",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Tue Mar 7 11:48:04 MST 2000",
  bibsource =    "http://www.idealibrary.com/cgi-bin/links/toc/sy;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production;
                 http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/pdf;
                 http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/ref",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
}


bibtype: inproceedings
filename: elefunt.bib
label: Cornea-Hasegan:1999:CPO
author: M. A. Cornea-Hasegan and R. A. Golliver and P. Markstein
crossref: Koren:1999:ISC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 96--105
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
keywords: ARITH; computer arithmetic; IEEE
acknowledgement: ack-nhfb
rawauthor: M. A. Cornea-Hasegan and R. A. Golliver and P. Markstein
title:
Correctness proofs outline for Newton--Raphson based floating-point divide and square root algorithms

URL:
http://euler.ecs.umass.edu/paper/final/paper-121.pdf; http://euler.ecs.umass.edu/paper/final/paper-121.ps

rawtitle:
Correctness proofs outline for {Newton--Raphson} based floating-point divide and square root algorithms

entry:
@InProceedings{Cornea-Hasegan:1999:CPO,
  author =       "M. A. Cornea-Hasegan and R. A. Golliver and P.
                 Markstein",
  title =        "Correctness proofs outline for {Newton--Raphson} based
                 floating-point divide and square root algorithms",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "96--105",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-121.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-121.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
  summary =      "This paper describes a study of a class of algorithms
                 for the floating-point divide and square root
                 operations, based on the Newton--Raphson iterative
                 method. The two main goals were. (1) Proving the IEEE
                 correctness of these iterative floating-point
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Corsonello:1999:HPS
author: P. Corsonello and S. Perri
title: High performance square rooting circuit using hybrid radix-$2$ adders
journal: j-ELECT-LETTERS
volume: 35
number: 3
pages: 185--186
day: 4
month: feb
monthnumber: 2
year: 1999
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: P. Corsonello and S. Perri
rawtitle: High performance square rooting circuit using hybrid radix-$2$ adders
entry:
@Article{Corsonello:1999:HPS,
  author =       "P. Corsonello and S. Perri",
  title =        "High performance square rooting circuit using hybrid
                 radix-$2$ adders",
  journal =      j-ELECT-LETTERS,
  volume =       "35",
  number =       "3",
  pages =        "185--186",
  day =          "4",
  month =        feb,
  year =         "1999",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "A new high performance bit parallel architecture for
                 computing square roots is proposed. The architecture
                 implements a non-restoring algorithm and is structured
                 as a pipelined cellular array. To improve the
                 performance, hybrid radix-$2$ adders are \ldots{}",
}


bibtype: techreport
filename: elefunt.bib
label: DiDonato:1999:TFC
author: Armido R. DiDonato and Russ Gnoffo
title: Testing a Fortran 90 Compiler Using the NSWC Fortran 77 Mathematics Library
type: Technical Report
number: NSWCDD/TR-98/75
institution: Naval Surface Warfare Center
address: Dahlgren, VA 22448-5100, USA
pages: v + 64
month: feb
monthnumber: 2
year: 1999
bibdate: Tue Jun 13 11:49:57 2023
bibtimestamp: 2023.06.13 11:49:57 ???
URL: https://apps.dtic.mil/sti/pdfs/ADA360604.pdf
acknowledgement: ack-nhfb
rawauthor: Armido R. DiDonato and Russ Gnoffo
rawtitle: Testing a {Fortran 90} Compiler Using the {NSWC Fortran 77 Mathematics Library}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/maple-extract.bib

abstract:
This report describes the analysis and associated Fortran program (TEST90) that were developed to aid in establishing the validity of a new Fortran 90 mainframe compiler. The FORTRAN 77 Naval Surface Warfare Center (NSWC) Mathematics library (MLJB) is used as a source of routines for checking the Fortran 90 compiler. At the same time, this study can be considered as an aid to determine whether MLIB can operate in a Fortran 90 environment. The inputs for the routines were chosen so that many of the different possible paths of the routines were executed. Seventy-four directly callable routines, with 293 supporting routines, were chosen for testing. All but 17, and their supporting routines, were taken from MLIB. The ones not belonging to MLIB, are double-precision versions of routines in MLIB. Thirteen hundred and twenty five numerical cases were submitted for testing. A true value for each test was obtained independently and given correctly to 35 digits by using MAPLE software. If the difference in the test output and the corresponding true value exceeds a prespecified error tolerance, an error message is printed identifying the routine and the input Additional test cases were also prepared to check the bit and string instructions, since these do not appear in MLIB.par TEST90 has been used to test the latest Fortran 90 compilers of the CRAY EL98 and IBM PC machines. No errors were found; however, TEST90 did reveal a complex arithmetic error in an earlier version of the Cray EL98 compiler. MLIB routines ran under TEST90 without any problems on both machines.par The transportability of MLIB allows TEST90 to be used as an aid in testing Fortran 90 compilers on a variety of computers, with a single-precision word length no larger than 64 bits.

rawabstract:
This report describes the analysis and associated Fortran program (TEST90) that were developed to aid in establishing the validity of a new Fortran 90 mainframe compiler. The FORTRAN 77 Naval Surface Warfare Center (NSWC) Mathematics library (MLJB) is used as a source of routines for checking the Fortran 90 compiler. At the same time, this study can be considered as an aid to determine whether MLIB can operate in a Fortran 90 environment. The inputs for the routines were chosen so that many of the different possible paths of the routines were executed. Seventy-four directly callable routines, with 293 supporting routines, were chosen for testing. All but 17, and their supporting routines, were taken from MLIB. The ones not belonging to MLIB, are double-precision versions of routines in MLIB. Thirteen hundred and twenty five numerical cases were submitted for testing. A true value for each test was obtained independently and given correctly to 35 digits by using MAPLE software. If the difference in the test output and the corresponding true value exceeds a prespecified error tolerance, an error message is printed identifying the routine and the input Additional test cases were also prepared to check the bit and string instructions, since these do not appear in MLIB.\par TEST90 has been used to test the latest Fortran 90 compilers of the CRAY EL98 and IBM PC machines. No errors were found; however, TEST90 did reveal a complex arithmetic error in an earlier version of the Cray EL98 compiler. MLIB routines ran under TEST90 without any problems on both machines.\par The transportability of MLIB allows TEST90 to be used as an aid in testing Fortran 90 compilers on a variety of computers, with a single-precision word length no larger than 64 bits.

entry:
@TechReport{DiDonato:1999:TFC,
  author =       "Armido R. DiDonato and Russ Gnoffo",
  title =        "Testing a {Fortran 90} Compiler Using the {NSWC
                 Fortran 77 Mathematics Library}",
  type =         "Technical Report",
  number =       "NSWCDD/TR-98/75",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5100, USA",
  pages =        "v + 64",
  month =        feb,
  year =         "1999",
  bibdate =      "Tue Jun 13 11:49:57 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  URL =          "https://apps.dtic.mil/sti/pdfs/ADA360604.pdf",
  abstract =     "This report describes the analysis and associated
                 Fortran program (TEST90) that were developed to aid in
                 establishing the validity of a new Fortran 90 mainframe
                 compiler. The FORTRAN 77 Naval Surface Warfare Center
                 (NSWC) Mathematics library (MLJB) is used as a source
                 of routines for checking the Fortran 90 compiler. At
                 the same time, this study can be considered as an aid
                 to determine whether MLIB can operate in a Fortran 90
                 environment. The inputs for the routines were chosen so
                 that many of the different possible paths of the
                 routines were executed. Seventy-four directly callable
                 routines, with 293 supporting routines, were chosen for
                 testing. All but 17, and their supporting routines,
                 were taken from MLIB. The ones not belonging to MLIB,
                 are double-precision versions of routines in MLIB.
                 Thirteen hundred and twenty five numerical cases were
                 submitted for testing. A true value for each test was
                 obtained independently and given correctly to 35 digits
                 by using MAPLE software. If the difference in the test
                 output and the corresponding true value exceeds a
                 prespecified error tolerance, an error message is
                 printed identifying the routine and the input
                 Additional test cases were also prepared to check the
                 bit and string instructions, since these do not appear
                 in MLIB.\par

                 TEST90 has been used to test the latest Fortran 90
                 compilers of the CRAY EL98 and IBM PC machines. No
                 errors were found; however, TEST90 did reveal a complex
                 arithmetic error in an earlier version of the Cray EL98
                 compiler. MLIB routines ran under TEST90 without any
                 problems on both machines.\par

                 The transportability of MLIB allows TEST90 to be used
                 as an aid in testing Fortran 90 compilers on a variety
                 of computers, with a single-precision word length no
                 larger than 64 bits.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Elbert:1999:SFZ
author: Arpad Elbert and Panayiotis D. Siafarikas
title: On the Square of the First Zero of the Bessel Function $ J_nu (z) $
journal: j-CAN-MATH-BULL
volume: 42
number: 1
pages: 56--77
month: mar
monthnumber: 3
year: 1999
CODEN: CMBUA3
DOI: https://doi.org/10.4153/CMB-1999-007-4
ISSN: 0008-4395 (print), 1496-4287 (electronic) OR 00084395 (print), 14964287 (electronic)
ISSNL: 0008-4395 OR 00084395
MRclass: 33A40
bibdate: Thu Sep 8 10:22:25 MDT 2011
bibtimestamp: 2011.09.08 10:22:25 MDT
fjournal: Canadian mathematical bulletin = Bulletin canadien de mathematiques
acknowledgement: ack-nhfb
journalURL: http://cms.math.ca/cmb/
rawauthor: {\'A}rp{\'a}d Elbert and Panayiotis D. Siafarikas
rawtitle: On the Square of the First Zero of the {Bessel} Function {$ J_\nu (z) $}
bibsource:
http://cms.math.ca/cmb/v42/; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
Let $ j_nu , 1 $ be the smallest (first) positive zero of the Bessel function $ J_nu (z) $, $ nu > - 1 $, which becomes zero when $ nu $ approaches $ - 1 $. Then $ j_nu , 1^2 $ can be continued analytically to $ - 2 < nu < - 1 $, where it takes on negative values. We show that $ j_nu , 1^2 $ is a convex function of $ nu $ in the interval $ - 2 < nu leq 0 $, as an addition to an old result [A. Elbert and A. Laforgia, SIAM J. Math. Anal. bf 15(1984), 206--212], stating this convexity for $ nu > 0 $. Also the monotonicity properties of the functions $ frac j_nu , 1^24 (nu + 1) $, $ frac j_nu , 1^24(nu + 1) sqrt nu + 2 $ are determined. Our approach is based on the series expansion of Bessel function $ J_nu (z) $ and it turned out to be effective, especially when $ - 2 < nu < - 1 $.

rawabstract:
Let $ j_{\nu, 1} $ be the smallest (first) positive zero of the Bessel function $ J_{\nu }(z) $, $ \nu > - 1 $, which becomes zero when $ \nu $ approaches $ - 1 $. Then $ j_{\nu, 1}^2 $ can be continued analytically to $ - 2 < \nu < - 1 $, where it takes on negative values. We show that $ j_{\nu, 1}^2 $ is a convex function of $ \nu $ in the interval $ - 2 < \nu \leq 0 $, as an addition to an old result [{\'A}. Elbert and A. Laforgia, SIAM J. Math. Anal. {\bf 15}(1984), 206--212], stating this convexity for $ \nu > 0 $. Also the monotonicity properties of the functions $ \frac {j_{\nu, 1}^24 (\nu + 1)} $, $ \frac {j_{\nu, 1}^24(\nu + 1) \sqrt {\nu + 2}} $ are determined. Our approach is based on the series expansion of Bessel function $ J_{\nu }(z) $ and it turned out to be effective, especially when $ - 2 < \nu < - 1 $.

entry:
@Article{Elbert:1999:SFZ,
  author =       "{\'A}rp{\'a}d Elbert and Panayiotis D. Siafarikas",
  title =        "On the Square of the First Zero of the {Bessel}
                 Function {$ J_\nu (z) $}",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "56--77",
  month =        mar,
  year =         "1999",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-1999-007-4",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "33A40",
  bibdate =      "Thu Sep 8 10:22:25 MDT 2011",
  bibsource =    "http://cms.math.ca/cmb/v42/;
                 https://www.math.utah.edu/pub/tex/bib/canmathbull.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Let $ j_{\nu, 1} $ be the smallest (first) positive
                 zero of the Bessel function $ J_{\nu }(z) $, $ \nu > -
                 1 $, which becomes zero when $ \nu $ approaches $ - 1
                 $. Then $ j_{\nu, 1}^2 $ can be continued analytically
                 to $ - 2 < \nu < - 1 $, where it takes on negative
                 values. We show that $ j_{\nu, 1}^2 $ is a convex
                 function of $ \nu $ in the interval $ - 2 < \nu \leq 0
                 $, as an addition to an old result [{\'A}. Elbert and
                 A. Laforgia, SIAM J. Math. Anal. {\bf 15}(1984),
                 206--212], stating this convexity for $ \nu > 0 $. Also
                 the monotonicity properties of the functions $ \frac
                 {j_{\nu, 1}^24 (\nu + 1)} $, $ \frac {j_{\nu, 1}^24(\nu
                 + 1) \sqrt {\nu + 2}} $ are determined. Our approach is
                 based on the series expansion of Bessel function $
                 J_{\nu }(z) $ and it turned out to be effective,
                 especially when $ - 2 < \nu < - 1 $.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "33A40",
  fjournal =     "Canadian mathematical bulletin = Bulletin canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
  journalabbrev = "CMB",
  refnum =       "7139",
  xxpages =      "56--67",
}


bibtype: techreport
filename: elefunt.bib
label: Ercegovac:1999:IGD
author: Milos D. Ercegovac and Laurent Imbert and David W. Matula and Jean-Michel Muller and Guoheng Wei
title: Improving Goldschmidt Division, Square Root, and Square Root Reciprocal
type: Research Report
number: 99-41
institution: Laboratoire de l'Informatique du Parallelisme
address: Lyon, France
pages: ii + 17
month: sep
monthnumber: 9
year: 1999
bibdate: Mon Dec 11 07:53:15 2023
bibtimestamp: 2023.12.11 07:53:15 ???
URL: https://inria.hal.science/inria-00072909/file/RR1999-41.pdf
acknowledgement: ack-nhfb
rawtitle: Improving {Goldschmidt} Division, Square Root, and Square Root Reciprocal
abstract:
The aim of this paper is to accelerate division, square root and square root reciprocal computations, when Goldschmidt method is used on a pipelined multiplier. This is done by replacing the last iteration by the addition of a correcting term that can be looked up during the early iterations. We describe several variants of the Goldschmidt algorithm assuming 4-cycle pipelined multiplier and discuss obtained number of cycles and error achieved. Extensions to other than 4-cycle multipliers are given

keywords:
Computer Arithmetic; Convergence division; Division; Goldschmidt iteration; Square root; Square root reciprocal

rawabstract:
The aim of this paper is to accelerate division, square root and square root reciprocal computations, when Goldschmidt method is used on a pipelined multiplier. This is done by replacing the last iteration by the addition of a correcting term that can be looked up during the early iterations. We describe several variants of the Goldschmidt algorithm assuming 4-cycle pipelined multiplier and discuss obtained number of cycles and error achieved. Extensions to other than 4-cycle multipliers are given

rawauthor:
Milo{\v{s}} D. Ercegovac and Laurent Imbert and David W. Matula and Jean-Michel Muller and Guoheng Wei

entry:
@TechReport{Ercegovac:1999:IGD,
  author =       "Milo{\v{s}} D. Ercegovac and Laurent Imbert and David
                 W. Matula and Jean-Michel Muller and Guoheng Wei",
  title =        "Improving {Goldschmidt} Division, Square Root, and
                 Square Root Reciprocal",
  type =         "Research Report",
  number =       "99-41",
  institution =  "Laboratoire de l'Informatique du Parall{\'e}lisme",
  address =      "Lyon, France",
  pages =        "ii + 17",
  month =        sep,
  year =         "1999",
  bibdate =      "Mon Dec 11 07:53:15 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/inria-00072909/file/RR1999-41.pdf",
  abstract =     "The aim of this paper is to accelerate division,
                 square root and square root reciprocal computations,
                 when Goldschmidt method is used on a pipelined
                 multiplier. This is done by replacing the last
                 iteration by the addition of a correcting term that can
                 be looked up during the early iterations. We describe
                 several variants of the Goldschmidt algorithm assuming
                 4-cycle pipelined multiplier and discuss obtained
                 number of cycles and error achieved. Extensions to
                 other than 4-cycle multipliers are given",
  acknowledgement = ack-nhfb,
  keywords =     "Computer Arithmetic; Convergence division; Division;
                 Goldschmidt iteration; Square root; Square root
                 reciprocal",
}


bibtype: article
filename: elefunt.bib
label: Fabijonas:1999:RAE
author: Bruce R. Fabijonas and F. W. J. Olver
title: On the Reversion of an Asymptotic Expansion and the Zeros of the Airy Functions
journal: j-SIAM-REVIEW
volume: 41
number: 4
pages: 762--773
month: dec
monthnumber: 12
year: 1999
CODEN: SIREAD
DOI: https://doi.org/10.1137/S0036144598349538
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Fri Jun 21 11:25:02 MDT 2013
bibtimestamp: 2013.06.21 11:25:02 MDT
URL: http://epubs.siam.org/sam-bin/dbq/article/34953
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: Dec-1999
rawauthor: Bruce R. Fabijonas and F. W. J. Olver
rawtitle: On the Reversion of an Asymptotic Expansion and the Zeros of the {Airy} Functions
bibsource:
http://epubs.siam.org/toc/siread/41/4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Fabijonas:1999:RAE,
  author =       "Bruce R. Fabijonas and F. W. J. Olver",
  title =        "On the Reversion of an Asymptotic Expansion and the
                 Zeros of the {Airy} Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "41",
  number =       "4",
  pages =        "762--773",
  month =        dec,
  year =         "1999",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/S0036144598349538",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "http://epubs.siam.org/toc/siread/41/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/34953",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "Dec-1999",
}


bibtype: article
filename: elefunt.bib
label: Fuller:1999:HVH
author: A. Thomas Fuller
title: Horner versus Holdred: an Episode in the History of Root Computation
journal: j-HIST-MATH
volume: 26
number: 1
pages: 29--51
day: 1
month: feb
monthnumber: 2
year: 1999
CODEN: HIMADS
ISSN: 0315-0860 (print), 1090-249X (electronic) OR 03150860 (print), 1090249X (electronic)
ISSNL: 0315-0860 OR 03150860
bibdate: Wed Jun 26 06:19:37 MDT 2013
bibtimestamp: 2013.06.26 06:19:37 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0315086098922145
fjournal: Historia Mathematica
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03150860
rawauthor: A. Thomas Fuller
rawtitle: {Horner} versus {Holdred}: an Episode in the History of Root Computation
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib

entry:
@Article{Fuller:1999:HVH,
  author =       "A. Thomas Fuller",
  title =        "{Horner} versus {Holdred}: an Episode in the History
                 of Root Computation",
  journal =      j-HIST-MATH,
  volume =       "26",
  number =       "1",
  pages =        "29--51",
  day =          "1",
  month =        feb,
  year =         "1999",
  CODEN =        "HIMADS",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:19:37 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086098922145",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1999:NRC
author: Walter Gautschi
title: A Note on the Recursive Calculation of Incomplete Gamma Functions
journal: j-TOMS
volume: 25
number: 1
pages: 101--107
month: mar
monthnumber: 3
year: 1999
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Jul 15 19:01:02 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.07.15 19:01:02 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; reliability
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Walter Gautschi
rawtitle: A Note on the Recursive Calculation of Incomplete Gamma Functions
URL:
http://doi.acm.org/10.1145/305658.305717; http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Gautschi:1999:NRC; http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p101-gautschi/

abstract:
It is known that the recurrence relation for incomplete gamma functions $ Gamma (a + n, x), 0 le a < 1 $, $ n = 0, 1, 2 ldots $, when $x$ is positive, is unstable---more so the larger $x$. Nevertheless, the recursion can be used in the range $ 0 le n le x $ practically without error growth, and in larger ranges $ 0 le n le N $ with a loss of accuracy that can be controlled by suitably limiting $N$.

subject:
bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Stability (and instability). bf G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.

rawabstract:
It is known that the recurrence relation for incomplete gamma functions $ \Gamma (a + n, x), 0 \le a < 1 $, $ n = 0, 1, 2 \ldots $, when $x$ is positive, is unstable---more so the larger $x$. Nevertheless, the recursion can be used in the range $ 0 \le n \le x $ practically without error growth, and in larger ranges $ 0 \le n \le N $ with a loss of accuracy that can be controlled by suitably limiting $N$.

entry:
@Article{Gautschi:1999:NRC,
  author =       "Walter Gautschi",
  title =        "A Note on the Recursive Calculation of Incomplete
                 Gamma Functions",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "101--107",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://doi.acm.org/10.1145/305658.305717;
                 http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Gautschi:1999:NRC;
                 http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p101-gautschi/",
  abstract =     "It is known that the recurrence relation for
                 incomplete gamma functions $ \Gamma (a + n, x), 0 \le a
                 < 1 $, $ n = 0, 1, 2 \ldots $, when $x$ is positive, is
                 unstable---more so the larger $x$. Nevertheless, the
                 recursion can be used in the range $ 0 \le n \le x $
                 practically without error growth, and in larger ranges
                 $ 0 \le n \le N $ with a loss of accuracy that can be
                 controlled by suitably limiting $N$.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; reliability",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Stability (and instability). {\bf
                 G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation.",
}


bibtype: techreport
filename: elefunt.bib
label: Gourdon:1999:NCC
author: Xavier Gourdon and Pascal Sebah
title: Numbers, constants, and computation
address: Paris, France
pages: 101--107
year: 1999
bibdate: Sat Mar 15 16:28:07 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2003.03.15 16:28:07 ???
note: World-Wide Web site.
URL: http://numbers.computation.free.fr/Constants/home.html
acknowledgement: ack-nhfb
rawauthor: Xavier Gourdon and Pascal Sebah
rawnote: World-Wide Web site.
rawtitle: Numbers, constants, and computation
annote:
Although this site concentrates mainly on computation of particular mathematical constants, it also treats high-precision computation of inverse and square root.

entry:
@TechReport{Gourdon:1999:NCC,
  author =       "Xavier Gourdon and Pascal Sebah",
  title =        "Numbers, constants, and computation",
  institution =  "????",
  address =      "Paris, France",
  year =         "1999",
  bibdate =      "Sat Mar 15 16:28:07 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "World-Wide Web site.",
  URL =          "http://numbers.computation.free.fr/Constants/home.html",
  acknowledgement = ack-nhfb,
  annote =       "Although this site concentrates mainly on computation
                 of particular mathematical constants, it also treats
                 high-precision computation of inverse and square
                 root.",
}


bibtype: article
filename: elefunt.bib
label: Harrison:1999:CTF
author: John Harrison and Ted Kubaska and Shane Story and Ping Tak Peter Tang
title: The Computation of Transcendental Functions on the IA-64 Architecture
journal: j-INTEL-TECH-J
number: Q4
pages: 7
day: 22
month: nov
monthnumber: 11
year: 1999
bibdate: Fri Jun 01 06:02:08 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2001.06.01 06:02:08 ???
acknowledgement: ack-nhfb
rawauthor: John Harrison and Ted Kubaska and Shane Story and Ping Tak Peter Tang
rawtitle: The Computation of Transcendental Functions on the {IA-64} Architecture
URL:
http://developer.intel.com/technology/itj/q41999/articles/art_5.htm; http://developer.intel.com/technology/itj/q41999/pdf/transendental.pdf

entry:
@Article{Harrison:1999:CTF,
  author =       "John Harrison and Ted Kubaska and Shane Story and Ping
                 Tak Peter Tang",
  title =        "The Computation of Transcendental Functions on the
                 {IA-64} Architecture",
  journal =      j-INTEL-TECH-J,
  number =       "Q4",
  pages =        "7",
  day =          "22",
  month =        nov,
  year =         "1999",
  bibdate =      "Fri Jun 01 06:02:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://developer.intel.com/technology/itj/q41999/articles/art_5.htm;
                 http://developer.intel.com/technology/itj/q41999/pdf/transendental.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Hayashi:1999:SRR
author: Takao Hayashi
journal: j-HIST-SCI-2
volume: 9
number: 2
pages: 135--153
month: nov
monthnumber: 11
year: 1999
CODEN: HISCDU
ISSN: 0285-4821 OR 02854821
ISSNL: 0285-4821 OR 02854821
MRclass: 01A32
MRnumber: 1762168
MRreviewer: A. I. Volodarski{\u\i}
bibdate: Sat Oct 6 17:22:25 2018
bibtimestamp: 2018.10.06 17:22:25 ???
acknowledgement: ack-nhfb
journalURL: http://hssj.info/
rawauthor: Takao Hayashi
title:
A set of rules for the root-extraction prescribed by the sixteenth-century Indian mathematicians, Nilakantha Somastuvan and Sankara Variyar

bibsource:
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/histscijpn.bib

fjournal:
Historia Scientiarum. Second Series. International Journal of the History of Science Society of Japan

rawtitle:
A set of rules for the root-extraction prescribed by the sixteenth-century {Indian} mathematicians, {N{\=\i}laka{\d{n}}{\d{t}}ha Somastuvan} and {{\'S}a{\.n}kara V{\=a}riyar}

entry:
@Article{Hayashi:1999:SRR,
  author =       "Takao Hayashi",
  title =        "A set of rules for the root-extraction prescribed by
                 the sixteenth-century {Indian} mathematicians,
                 {N{\=\i}laka{\d{n}}{\d{t}}ha Somastuvan} and
                 {{\'S}a{\.n}kara V{\=a}riyar}",
  journal =      j-HIST-SCI-2,
  volume =       "9",
  number =       "2",
  pages =        "135--153",
  month =        nov,
  year =         "1999",
  CODEN =        "HISCDU",
  ISSN =         "0285-4821",
  ISSN-L =       "0285-4821",
  MRclass =      "01A32",
  MRnumber =     "1762168",
  MRreviewer =   "A. I. Volodarski{\u\i}",
  bibdate =      "Sat Oct 6 17:22:25 2018",
  bibsource =    "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/histscijpn.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Scientiarum. Second Series. International
                 Journal of the History of Science Society of Japan",
  journal-URL =  "http://hssj.info/",
}


bibtype: article
filename: elefunt.bib
label: Homeier:1999:CAL
author: H. H. H. Homeier
title: Convergence acceleration of logarithmically convergent series avoiding summation
journal: j-APPL-MATH-LETT
volume: 12
number: 3
pages: 29--32
year: 1999
CODEN: AMLEEL
DOI: https://doi.org/10.1016/S0893-9659(98)00167-0
ISSN: 0893-9659 (print), 1873-5452 (electronic) OR 08939659 (print), 18735452 (electronic)
ISSNL: 0893-9659 OR 08939659
MRclass: 65B05
MRnumber: 1749733
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: Applied Mathematics Letters
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08939659
rawauthor: H. H. H. Homeier
rawtitle: Convergence acceleration of logarithmically convergent series avoiding summation
entry:
@Article{Homeier:1999:CAL,
  author =       "H. H. H. Homeier",
  title =        "Convergence acceleration of logarithmically convergent
                 series avoiding summation",
  journal =      j-APPL-MATH-LETT,
  volume =       "12",
  number =       "3",
  pages =        "29--32",
  year =         "1999",
  CODEN =        "AMLEEL",
  DOI =          "https://doi.org/10.1016/S0893-9659(98)00167-0",
  ISSN =         "0893-9659 (print), 1873-5452 (electronic)",
  ISSN-L =       "0893-9659",
  MRclass =      "65B05",
  MRnumber =     "1749733",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08939659",
  keywords =     "convergence acceleration",
}


bibtype: inproceedings
filename: elefunt.bib
label: Hyogo:1999:LVF
author: A. Hyogo and Y. Fukutomi and K. Sekine
title: Low voltage four-quadrant analog multiplier using square-root circuit based on CMOS pair
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 274--277
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: A. Hyogo and Y. Fukutomi and K. Sekine
rawtitle: Low voltage four-quadrant analog multiplier using square-root circuit based on {CMOS} pair
booktitle:
Proceedings of the 1999 IEEE International Symposium on Circuits and Systems: ISCAS '99, 2 June 1999

rawbooktitle:
Proceedings of the 1999 {IEEE} International Symposium on Circuits and Systems: {ISCAS '99}, 2 June 1999

entry:
@InProceedings{Hyogo:1999:LVF,
  author =       "A. Hyogo and Y. Fukutomi and K. Sekine",
  booktitle =    "Proceedings of the 1999 {IEEE} International Symposium
                 on Circuits and Systems: {ISCAS '99}, 2 June 1999",
  title =        "Low voltage four-quadrant analog multiplier using
                 square-root circuit based on {CMOS} pair",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "274--277",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We proposed a square-root circuit based on CMOS pairs.
                 In this paper, we propose a low voltage four-quadrant
                 analog multiplier using the square-root circuit. Also
                 we confirmed this operation by PSpice \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Iordache:1999:ARS
author: Cristina Iordache and David W. Matula
journal: j-ELECT-NOTES-THEOR-COMP-SCI
volume: 24
pages: 34--62
year: 1999
DOI: https://doi.org/10.1016/S1571-0661(05)80621-8
ISSN: 1571-0661 OR 15710661
bibdate: Fri Jun 24 20:23:13 2005
bibtimestamp: 2005.06.24 20:23:13 ???
fjournal: Electronic Notes in Theoretical Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/15710661
rawauthor: Cristina Iordache and David W. Matula
title:
Analysis of Reciprocal and Square Root Reciprocal Instructions in the AMD K6-2 Implementation of 3DNow!

abstract:
Reciprocal and root reciprocal functions at ``half'' and IEEE single precision formats are specified in the AMD 3DNow! instruction set. Implementations in the recently released AMD K6-2 microprocessor are analyzed herein by exhaustive computation and timing loops to ascertain the accuracy and monotonicity properties of the output and throughput / latency cycle counts. Periodicities in stepwise function output were observed and employed to construct an underlying bipartite table that can serve as the core of the respective reciprocal function outputs. The recommended RISC instruction macros generated single precision reciprocals and root reciprocals accurate to a unit in the last place. However, the root reciprocal functions failed to satisfy the desirable monotonicity property typically implemented as an industry standard for elementary functions on x86 floating point units. Reasons for the failure are provided and an adjusted table is shown to satisfy the monotonicity standard. Results are summarized in Table 1 and described in the body of this report.

rawabstract:
Reciprocal and root reciprocal functions at ``half'' and IEEE single precision formats are specified in the AMD 3DNow! instruction set. Implementations in the recently released AMD K6-2 microprocessor are analyzed herein by exhaustive computation and timing loops to ascertain the accuracy and monotonicity properties of the output and throughput\slash latency cycle counts. Periodicities in stepwise function output were observed and employed to construct an underlying bipartite table that can serve as the core of the respective reciprocal function outputs. The recommended RISC instruction macros generated single precision reciprocals and root reciprocals accurate to a unit in the last place. However, the root reciprocal functions failed to satisfy the desirable monotonicity property typically implemented as an industry standard for elementary functions on x86 floating point units. Reasons for the failure are provided and an adjusted table is shown to satisfy the monotonicity standard. Results are summarized in Table 1 and described in the body of this report.

rawtitle:
Analysis of Reciprocal and Square Root Reciprocal Instructions in the {AMD K6-2} Implementation of {3DNow!}

entry:
@Article{Iordache:1999:ARS,
  author =       "Cristina Iordache and David W. Matula",
  title =        "Analysis of Reciprocal and Square Root Reciprocal
                 Instructions in the {AMD K6-2} Implementation of
                 {3DNow!}",
  journal =      j-ELECT-NOTES-THEOR-COMP-SCI,
  volume =       "24",
  pages =        "34--62",
  year =         "1999",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/S1571-0661(05)80621-8",
  ISSN =         "1571-0661",
  bibdate =      "Fri Jun 24 20:23:13 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Reciprocal and root reciprocal functions at ``half''
                 and IEEE single precision formats are specified in the
                 AMD 3DNow! instruction set. Implementations in the
                 recently released AMD K6-2 microprocessor are analyzed
                 herein by exhaustive computation and timing loops to
                 ascertain the accuracy and monotonicity properties of
                 the output and throughput\slash latency cycle counts.
                 Periodicities in stepwise function output were observed
                 and employed to construct an underlying bipartite table
                 that can serve as the core of the respective reciprocal
                 function outputs. The recommended RISC instruction
                 macros generated single precision reciprocals and root
                 reciprocals accurate to a unit in the last place.
                 However, the root reciprocal functions failed to
                 satisfy the desirable monotonicity property typically
                 implemented as an industry standard for elementary
                 functions on x86 floating point units. Reasons for the
                 failure are provided and an adjusted table is shown to
                 satisfy the monotonicity standard. Results are
                 summarized in Table 1 and described in the body of this
                 report.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Notes in Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15710661",
}


bibtype: inproceedings
filename: elefunt.bib
label: Iordache:1999:IPR
author: Cristina Iordache and David W. Matula
title: On Infinitely Precise Rounding for Division, Square Root, Reciprocal and Square Root Reciprocal
crossref: Koren:1999:ISC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 233--240
year: 1999
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
keywords: ARITH-14; computer arithmetic; IEEE
acknowledgement: ack-nhfb
rawauthor: Cristina Iordache and David W. Matula
rawtitle: On Infinitely Precise Rounding for Division, Square Root, Reciprocal and Square Root Reciprocal
URL:
http://euler.ecs.umass.edu/paper/final/paper-164.pdf; http://euler.ecs.umass.edu/paper/final/paper-164.ps; http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Iordache.pdf

abstract:
Quotients, reciprocals, square roots and square root reciprocals all have the property that infinitely precise p-bit rounded results for p-bit input operands can be obtained from approximate results of bounded accuracy. We investigate lower bounds on the number of bits of an approximation accurate to a unit in the last place sufficient to guarantee that correct round and sticky bits can be determined. Known lower bounds for quotients and square roots are given and/or sharpened, and a new lower bound for root reciprocals is proved. Specifically for reciprocals, quotients and square roots, tight bounds of order $ 2 p + O(1) $ are presented. For infinitely precise rounding of the root reciprocal a lower bound can be found at $ 3 p + O(1) $, but exhaustive testing for small sizes of the operand suggests that in practice $ (2 + epsilon )p $ for small $ epsilon $ is usually sufficient. Algorithms can be designed for obtaining the round and sticky bits based on the bit pattern of an approximation computed to the required accuracy. We show that some improvement of the known lower bound for reciprocals and division is achievable at the cost of somewhat more complex hardware for rounding. Tests for the exactness of the quotient and square root are also provided.

rawabstract:
Quotients, reciprocals, square roots and square root reciprocals all have the property that infinitely precise p-bit rounded results for p-bit input operands can be obtained from approximate results of bounded accuracy. We investigate lower bounds on the number of bits of an approximation accurate to a unit in the last place sufficient to guarantee that correct round and sticky bits can be determined. Known lower bounds for quotients and square roots are given and/or sharpened, and a new lower bound for root reciprocals is proved. Specifically for reciprocals, quotients and square roots, tight bounds of order $ 2 p + O(1) $ are presented. For infinitely precise rounding of the root reciprocal a lower bound can be found at $ 3 p + O(1) $, but exhaustive testing for small sizes of the operand suggests that in practice $ (2 + \epsilon)p $ for small $ \epsilon $ is usually sufficient. Algorithms can be designed for obtaining the round and sticky bits based on the bit pattern of an approximation computed to the required accuracy. We show that some improvement of the known lower bound for reciprocals and division is achievable at the cost of somewhat more complex hardware for rounding. Tests for the exactness of the quotient and square root are also provided.

entry:
@InProceedings{Iordache:1999:IPR,
  author =       "Cristina Iordache and David W. Matula",
  title =        "On Infinitely Precise Rounding for Division, Square
                 Root, Reciprocal and Square Root Reciprocal",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "233--240",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-164.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-164.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Iordache.pdf",
  abstract =     "Quotients, reciprocals, square roots and square root
                 reciprocals all have the property that infinitely
                 precise p-bit rounded results for p-bit input operands
                 can be obtained from approximate results of bounded
                 accuracy. We investigate lower bounds on the number of
                 bits of an approximation accurate to a unit in the last
                 place sufficient to guarantee that correct round and
                 sticky bits can be determined. Known lower bounds for
                 quotients and square roots are given and/or sharpened,
                 and a new lower bound for root reciprocals is proved.
                 Specifically for reciprocals, quotients and square
                 roots, tight bounds of order $ 2 p + O(1) $ are
                 presented. For infinitely precise rounding of the root
                 reciprocal a lower bound can be found at $ 3 p + O(1)
                 $, but exhaustive testing for small sizes of the
                 operand suggests that in practice $ (2 + \epsilon)p $
                 for small $ \epsilon $ is usually sufficient.
                 Algorithms can be designed for obtaining the round and
                 sticky bits based on the bit pattern of an
                 approximation computed to the required accuracy. We
                 show that some improvement of the known lower bound for
                 reciprocals and division is achievable at the cost of
                 somewhat more complex hardware for rounding. Tests for
                 the exactness of the quotient and square root are also
                 provided.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic; IEEE",
  summary =      "Quotients, reciprocals, square roots and square root
                 reciprocals all have the property that infinitely
                 precise p-bit rounded results for p-bit input operands
                 can be obtained from approximate results of bounded
                 accuracy. We investigate lower bounds \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Jamieson:1999:NRF
author: M. J. Jamieson
title: Notes: On rational function approximations to square roots
journal: j-AMER-MATH-MONTHLY
volume: 106
number: 1
pages: 50--52
month: jan
monthnumber: 1
year: 1999
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 11Yxx
MRnumber: 1 674 202
bibdate: Tue Jun 22 10:29:34 MDT 1999
bibtimestamp: 1999.06.22 10:29:34 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: M. J. Jamieson
rawtitle: Notes: On rational function approximations to square roots
entry:
@Article{Jamieson:1999:NRF,
  author =       "M. J. Jamieson",
  title =        "Notes: On rational function approximations to square
                 roots",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "106",
  number =       "1",
  pages =        "50--52",
  month =        jan,
  year =         "1999",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11Yxx",
  MRnumber =     "1 674 202",
  bibdate =      "Tue Jun 22 10:29:34 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: book
filename: elefunt.bib
label: Jeffreys:1999:MMP
author: Harold Jeffreys and Bertha Swirles Jeffreys
title: Methods of Mathematical Physics
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
edition: Third
pages: viii + 718
year: 1999
ISBN: 0-521-66402-0 (paperback) OR 0521664020 (paperback)
ISBN13: 978-0-521-66402-8 (paperback) OR 9780521664028 (paperback)
LCCN: QA401 .J4 1999
bibdate: Thu Aug 17 10:48:45 2023
bibtimestamp: 2023.08.17 10:48:45 ???
note: Reprint of cite Jeffreys:1956:MMP.
URL: https://en.wikipedia.org/wiki/Bertha_Swirles; https://en.wikipedia.org/wiki/Harold_Jeffreys
acknowledgement: ack-nhfb
subjectdates: Douglas Rayner Hartree (27 March 1897--12 February 1958)
rawauthor: Harold Jeffreys and Bertha {Swirles Jeffreys}
rawnote: Reprint of \cite{Jeffreys:1956:MMP}.
rawtitle: Methods of Mathematical Physics
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib

remark:
First edition 1946, second edition 1950, third edition 1956, first paperback edition 1972, reprinted 1978, 1980, 1988, 1992, 1999, 2001. Third edition preface is dated April 1953. Second edition preface is dated 15 November 1948. First edition preface is dated 1946.

TOC:
Preface Authors' Notes 1: The Real Variable 2: Scalars and Vectors 3: Tensors 4: Matrices 5: Multiple Integrals 6: Potential Theory 7: Operational Methods 8: Physical Applications of the Operational Method 9: Numerical Methods 10: Calculus of Variations 11: Functions of a Complex Variable 12: Contour Integration and Bromwich's Integral 13: Conformal Representation 14: Fourier's Theorem 15: The Factorial and Related Functions 16: Solution of Linear Differential Equation 17: Asymptotic Expansions 18: The Equations of Potential, Waves, and Heat Conduction 19: Waves in One Dimension and Waves With Spherical Symmetry 20: Conduction of Heat in One and Three Dimensions 21: Bessel Functions 22: Applications of Bessel Functions 23: The Confluent Hypergeometric Function 24: Legendre Functions and Associated Functions 25: Elliptic Functions Notes Appendix on Notation Index

authordates:
Sir Harold Jeffreys (22 April 1891--18 March 1989); Lady Bertha Swirles Jeffreys (22 May 1903--18 December 1999)

rawTOC:
Preface \\ Authors' Notes \\ 1: The Real Variable \\ 2: Scalars and Vectors \\ 3: Tensors \\ 4: Matrices \\ 5: Multiple Integrals \\ 6: Potential Theory \\ 7: Operational Methods \\ 8: Physical Applications of the Operational Method \\ 9: Numerical Methods \\ 10: Calculus of Variations \\ 11: Functions of a Complex Variable \\ 12: Contour Integration and Bromwich's Integral \\ 13: Conformal Representation \\ 14: Fourier's Theorem \\ 15: The Factorial and Related Functions \\ 16: Solution of Linear Differential Equation \\ 17: Asymptotic Expansions \\ 18: The Equations of Potential, Waves, and Heat Conduction \\ 19: Waves in One Dimension and Waves With Spherical Symmetry \\ 20: Conduction of Heat in One and Three Dimensions \\ 21: Bessel Functions \\ 22: Applications of Bessel Functions \\ 23: The Confluent Hypergeometric Function \\ 24: Legendre Functions and Associated Functions \\ 25: Elliptic Functions \\ Notes \\ Appendix on Notation \\ Index

entry:
@Book{Jeffreys:1999:MMP,
  author =       "Harold Jeffreys and Bertha {Swirles Jeffreys}",
  title =        "Methods of Mathematical Physics",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Third",
  pages =        "viii + 718",
  year =         "1999",
  ISBN =         "0-521-66402-0 (paperback)",
  ISBN-13 =      "978-0-521-66402-8 (paperback)",
  LCCN =         "QA401 .J4 1999",
  bibdate =      "Thu Aug 17 10:48:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
  note =         "Reprint of \cite{Jeffreys:1956:MMP}.",
  URL =          "https://en.wikipedia.org/wiki/Bertha_Swirles;
                 https://en.wikipedia.org/wiki/Harold_Jeffreys",
  acknowledgement = ack-nhfb,
  author-dates = "Sir Harold Jeffreys (22 April 1891--18 March 1989);
                 Lady Bertha Swirles Jeffreys (22 May 1903--18 December
                 1999)",
  remark =       "First edition 1946, second edition 1950, third edition
                 1956, first paperback edition 1972, reprinted 1978,
                 1980, 1988, 1992, 1999, 2001. Third edition preface is
                 dated April 1953. Second edition preface is dated 15
                 November 1948. First edition preface is dated 1946.",
  subject-dates = "Douglas Rayner Hartree (27 March 1897--12 February
                 1958)",
  tableofcontents = "Preface \\
                 Authors' Notes \\
                 1: The Real Variable \\
                 2: Scalars and Vectors \\
                 3: Tensors \\
                 4: Matrices \\
                 5: Multiple Integrals \\
                 6: Potential Theory \\
                 7: Operational Methods \\
                 8: Physical Applications of the Operational Method \\
                 9: Numerical Methods \\
                 10: Calculus of Variations \\
                 11: Functions of a Complex Variable \\
                 12: Contour Integration and Bromwich's Integral \\
                 13: Conformal Representation \\
                 14: Fourier's Theorem \\
                 15: The Factorial and Related Functions \\
                 16: Solution of Linear Differential Equation \\
                 17: Asymptotic Expansions \\
                 18: The Equations of Potential, Waves, and Heat
                 Conduction \\
                 19: Waves in One Dimension and Waves With Spherical
                 Symmetry \\
                 20: Conduction of Heat in One and Three Dimensions \\
                 21: Bessel Functions \\
                 22: Applications of Bessel Functions \\
                 23: The Confluent Hypergeometric Function \\
                 24: Legendre Functions and Associated Functions \\
                 25: Elliptic Functions \\
                 Notes \\
                 Appendix on Notation \\
                 Index",
}


bibtype: misc
filename: elefunt.bib
label: Kahan:1999:SRD
author: W. Kahan
title: Square Root Without Division
pages: 3
day: 23
month: feb
monthnumber: 2
year: 1999
bibdate: Mon Apr 25 18:01:49 2005
bibtimestamp: 2005.04.25 18:01:49 ???
URL: http://www.cs.berkeley.edu/~wkahan/ieee754status/reciprt.pdf
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: W. Kahan
rawtitle: Square Root Without Division
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Misc{Kahan:1999:SRD,
  author =       "W. Kahan",
  title =        "Square Root Without Division",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "23",
  month =        feb,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:01:49 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/reciprt.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Krukier:1999:CAT
author: L. A. Krukier
journal: j-APPL-NUM-MATH
volume: 30
number: 2--3
pages: 281--290
day: 10
month: jun
monthnumber: 6
year: 1999
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Wed Jul 28 14:37:31 MDT 1999
bibtimestamp: 1999.07.28 14:37:31 MDT
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: L. A. Krukier
title:
Convergence acceleration of triangular iterative methods based on the skew-symmetric part of the matrix

bibsource:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=30&issue=2-3; https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1999&volume=30&issue=2-3&aid=981

rawtitle:
Convergence acceleration of triangular iterative methods based on the skew-symmetric part of the matrix

entry:
@Article{Krukier:1999:CAT,
  author =       "L. A. Krukier",
  title =        "Convergence acceleration of triangular iterative
                 methods based on the skew-symmetric part of the
                 matrix",
  journal =      j-APPL-NUM-MATH,
  volume =       "30",
  number =       "2--3",
  pages =        "281--290",
  day =          "10",
  month =        jun,
  year =         "1999",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Wed Jul 28 14:37:31 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=30&issue=2-3;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1999&volume=30&issue=2-3&aid=981",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Kzaz:1999:CAG
author: M. Kzaz
title: Convergence acceleration of the Gauss--Laguerre quadrature formula
journal: j-APPL-NUM-MATH
volume: 29
number: 2
pages: 201--220
day: 1
month: feb
monthnumber: 2
year: 1999
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Wed Jul 28 14:37:22 MDT 1999
bibtimestamp: 1999.07.28 14:37:22 MDT
URL: http://www.elsevier.com/cas/tree/store/apnum/sub/1999/29/2/940.pdf
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: M. Kzaz
rawtitle: Convergence acceleration of the {Gauss--Laguerre} quadrature formula
bibsource:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=29&issue=2; https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Kzaz:1999:CAG,
  author =       "M. Kzaz",
  title =        "Convergence acceleration of the {Gauss--Laguerre}
                 quadrature formula",
  journal =      j-APPL-NUM-MATH,
  volume =       "29",
  number =       "2",
  pages =        "201--220",
  day =          "1",
  month =        feb,
  year =         "1999",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Wed Jul 28 14:37:22 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=29&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/cas/tree/store/apnum/sub/1999/29/2/940.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Lang:1999:VHR
author: T. Lang and P. Montuschi
title: Very high radix square root with prescaling and rounding and a combined division / square root unit
journal: j-IEEE-TRANS-COMPUT
volume: 48
number: 8
pages: 827--841
month: aug
monthnumber: 8
year: 1999
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.795124
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. Lang and P. Montuschi
rawtitle:
Very high radix square root with prescaling and rounding and a combined division\slash square root unit

entry:
@Article{Lang:1999:VHR,
  author =       "T. Lang and P. Montuschi",
  title =        "Very high radix square root with prescaling and
                 rounding and a combined division\slash square root
                 unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "8",
  pages =        "827--841",
  month =        aug,
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.795124",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An algorithm for square root with prescaling and
                 selection by rounding is developed and combined with a
                 similar scheme for division. Since division is usually
                 more frequent than square root, the main concern of the
                 combined implementation is to \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lee:1999:STS
author: Young-Sang Lee and Jun-Woo Kang and Lee-Sup Kim and Seung-Ho Hwang
booktitle: 6th International Conference on VLSI and CAD: ICVC '99
title: Self-timed shared division and square-root implementation using full redundant signed digit numbers
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 541--544
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Young-Sang Lee and Jun-Woo Kang and Lee-Sup Kim and Seung-Ho Hwang
rawbooktitle: 6th International Conference on {VLSI} and {CAD}: {ICVC '99}
rawtitle: Self-timed shared division and square-root implementation using full redundant signed digit numbers
entry:
@InProceedings{Lee:1999:STS,
  author =       "Young-Sang Lee and Jun-Woo Kang and Lee-Sup Kim and
                 Seung-Ho Hwang",
  booktitle =    "6th International Conference on {VLSI} and {CAD}:
                 {ICVC '99}",
  title =        "Self-timed shared division and square-root
                 implementation using full redundant signed digit
                 numbers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "541--544",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "A radix-$2$ square root implementation for self-timed
                 dividers using redundant signed-digit (RSD) adders is
                 presented. In this method, two self-timed RSD adder
                 stages are used for each result bit selection. A very
                 efficient and simple result bit \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lozier:1999:DDM
author: Daniel W. Lozier and B. R. Miller and B. V. Saunders
title: Design of a Digital Mathematical Library for Science, Technology and Education
crossref: IEEE:1999:PIF
pages: 118--128
year: 1999
bibdate: Fri Jul 09 06:33:35 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:33:35 ???
URL: http://dlmf.nist.gov/about/publications/nistir6297.ps.gz
remark: Preprint: NISTIR 6297, Feb. 1999, 13 pages
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier and B. R. Miller and B. V. Saunders
rawtitle: Design of a Digital Mathematical Library for Science, Technology and Education
entry:
@InProceedings{Lozier:1999:DDM,
  author =       "Daniel W. Lozier and B. R. Miller and B. V. Saunders",
  title =        "Design of a Digital Mathematical Library for Science,
                 Technology and Education",
  crossref =     "IEEE:1999:PIF",
  pages =        "118--128",
  year =         "1999",
  bibdate =      "Fri Jul 09 06:33:35 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://dlmf.nist.gov/about/publications/nistir6297.ps.gz",
  acknowledgement = ack-nhfb,
  remark =       "Preprint: NISTIR 6297, Feb. 1999, 13 pages",
}


bibtype: article
filename: elefunt.bib
label: Morita:1999:CEI
author: T. Morita
title: Calculation of the elliptic integrals of the first and second kinds with complex modulus
journal: j-NUM-MATH
volume: 82
number: 4
pages: 677--688
month: jun
monthnumber: 6
year: 1999
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon Oct 18 10:45:11 MDT 1999
bibtimestamp: 1999.10.18 10:45:11 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: T. Morita
rawtitle: Calculation of the elliptic integrals of the first and second kinds with complex modulus
bibsource:
http://link.springer-ny.com/link/service/journals/00211/tocs/t9082004.htm; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://link.springer-ny.com/link/service/journals/00211/bibs/9082004/90820677.htm; http://link.springer-ny.com/link/service/journals/00211/papers/9082004/90820677.pdf

entry:
@Article{Morita:1999:CEI,
  author =       "T. Morita",
  title =        "Calculation of the elliptic integrals of the first and
                 second kinds with complex modulus",
  journal =      j-NUM-MATH,
  volume =       "82",
  number =       "4",
  pages =        "677--688",
  month =        jun,
  year =         "1999",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 10:45:11 MDT 1999",
  bibsource =    "http://link.springer-ny.com/link/service/journals/00211/tocs/t9082004.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer-ny.com/link/service/journals/00211/bibs/9082004/90820677.htm;
                 http://link.springer-ny.com/link/service/journals/00211/papers/9082004/90820677.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Muller:1999:CAT
author: J. Muller
title: Convergence acceleration of Taylor sections by convolution
journal: j-CONST-APPROX
volume: 15
number: 4
pages: 523--536
year: 1999
DOI: https://doi.org/10.1007/s003659900120
ISSN: 0176-4276 (print), 1432-0940 (electronic) OR 01764276 (print), 14320940 (electronic)
ISSNL: 0176-4276 OR 01764276
MRclass: 41A58 (30E10)
MRnumber: 1702803 (2000i:41040)
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: Constructive Approximation
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/365
rawauthor: J. M{\"u}ller
rawtitle: Convergence acceleration of {Taylor} sections by convolution
entry:
@Article{Muller:1999:CAT,
  author =       "J. M{\"u}ller",
  title =        "Convergence acceleration of {Taylor} sections by
                 convolution",
  journal =      j-CONST-APPROX,
  volume =       "15",
  number =       "4",
  pages =        "523--536",
  year =         "1999",
  DOI =          "https://doi.org/10.1007/s003659900120",
  ISSN =         "0176-4276 (print), 1432-0940 (electronic)",
  ISSN-L =       "0176-4276",
  MRclass =      "41A58 (30E10)",
  MRnumber =     "1702803 (2000i:41040)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Constructive Approximation",
  journal-URL =  "http://link.springer.com/journal/365",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Muroi:1999:ESR
author: Kazuo Muroi
title: Extraction of square roots in Babylonian mathematics
journal: j-HIST-SCI-2
volume: 9
number: 2
pages: 127--133
month: nov
monthnumber: 11
year: 1999
CODEN: HISCDU
ISSN: 0285-4821 OR 02854821
ISSNL: 0285-4821 OR 02854821
MRclass: 01A17
MRnumber: 1762167
MRreviewer: Bruno Poizat
bibdate: Sat Oct 6 17:22:25 2018
bibtimestamp: 2018.10.06 17:22:25 ???
acknowledgement: ack-nhfb
journalURL: http://hssj.info/
rawauthor: Kazuo Muroi
rawtitle: Extraction of square roots in {Babylonian} mathematics
bibsource:
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/histscijpn.bib

fjournal:
Historia Scientiarum. Second Series. International Journal of the History of Science Society of Japan

entry:
@Article{Muroi:1999:ESR,
  author =       "Kazuo Muroi",
  title =        "Extraction of square roots in {Babylonian}
                 mathematics",
  journal =      j-HIST-SCI-2,
  volume =       "9",
  number =       "2",
  pages =        "127--133",
  month =        nov,
  year =         "1999",
  CODEN =        "HISCDU",
  ISSN =         "0285-4821",
  ISSN-L =       "0285-4821",
  MRclass =      "01A17",
  MRnumber =     "1762167",
  MRreviewer =   "Bruno Poizat",
  bibdate =      "Sat Oct 6 17:22:25 2018",
  bibsource =    "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/histscijpn.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Scientiarum. Second Series. International
                 Journal of the History of Science Society of Japan",
  journal-URL =  "http://hssj.info/",
}


bibtype: inproceedings
filename: elefunt.bib
label: Nannarelli:1999:LPR
author: A. Nannarelli and T. Lang
booktitle: (ICCD '99) International Conference on Computer Design
title: Low-power radix-$4$ combined division and square root
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 236--242
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: A. Nannarelli and T. Lang
rawbooktitle: {(ICCD '99)} International Conference on Computer Design
rawtitle: Low-power radix-$4$ combined division and square root
entry:
@InProceedings{Nannarelli:1999:LPR,
  author =       "A. Nannarelli and T. Lang",
  booktitle =    "{(ICCD '99)} International Conference on Computer
                 Design",
  title =        "Low-power radix-$4$ combined division and square
                 root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "236--242",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Because of the similarities in the algorithm it is
                 quite common to implement division and square root in
                 the same unit. The purpose of this work is to implement
                 a low-power combined radix-$4$ division and square root
                 floating-point double precision \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Oberman:1999:FPD
author: S. F. Oberman
crossref: Koren:1999:ISC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 106--115
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
keywords: ARITH; computer arithmetic; IEEE
acknowledgement: ack-nhfb
rawauthor: S. F. Oberman
title:
Floating point division and square root algorithms and implementation in the AMD-K7TM microprocessor

URL:
http://euler.ecs.umass.edu/paper/final/paper-139.pdf; http://euler.ecs.umass.edu/paper/final/paper-139.ps

rawtitle:
Floating point division and square root algorithms and implementation in the {AMD-K7{\TM}} microprocessor

entry:
@InProceedings{Oberman:1999:FPD,
  author =       "S. F. Oberman",
  title =        "Floating point division and square root algorithms and
                 implementation in the {AMD-K7{\TM}} microprocessor",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "106--115",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-139.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-139.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
  summary =      "This paper presents the AMD-K7 IEEE 754 and $\times$87
                 compliant floating point division and square root
                 algorithms and implementation. The AMD-K7 processor
                 employs an iterative implementation of a series
                 expansion to converge quadratically to the \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Parhami:1999:ALT
author: B. Parhami
booktitle: Conference Record of the Thirty-Third Asilomar Conference on Signals, Systems, and Computers, 1999
title: Analysis of the lookup table size for square-rooting
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1327--1330
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: B. Parhami
rawbooktitle: Conference Record of the Thirty-Third Asilomar Conference on Signals, Systems, and Computers, 1999
rawtitle: Analysis of the lookup table size for square-rooting
entry:
@InProceedings{Parhami:1999:ALT,
  author =       "B. Parhami",
  booktitle =    "Conference Record of the Thirty-Third Asilomar
                 Conference on Signals, Systems, and Computers, 1999",
  title =        "Analysis of the lookup table size for square-rooting",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1327--1330",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Convergence methods are widely used for division,
                 reciprocation, and square-rooting. With such methods,
                 it is common to use an initial table lookup step for
                 obtaining an approximate result that leads to faster
                 convergence. In the case of division \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Russinoff:1999:MCP
author: David M. Russinoff
title: A mechanically checked proof of correctness of the AMD K5 floating point square root microcode
journal: j-FORM-METHODS-SYST-DES
volume: 14
number: 1
pages: 75--125
month: jan
monthnumber: 1
year: 1999
CODEN: FMSDE6
ISSN: 0925-9856 (print), 1572-8102 (electronic) OR 09259856 (print), 15728102 (electronic)
ISSNL: 0925-9856 OR 09259856
bibdate: Sat Jun 02 07:51:51 2001
bibtimestamp: 2001.06.02 07:51:51 ???
note: Special issue on arithmetic circuits.
URL: http://www.wkap.nl/jrnltoc.htm/0925-9856; http://www.wkap.nl/oasis.htm/194808
fjournal: Formal Methods in System Design
acknowledgement: ack-nhfb
rawauthor: David M. Russinoff
rawnote: Special issue on arithmetic circuits.
rawtitle: A mechanically checked proof of correctness of the {AMD K5} floating point square root microcode
entry:
@Article{Russinoff:1999:MCP,
  author =       "David M. Russinoff",
  title =        "A mechanically checked proof of correctness of the
                 {AMD K5} floating point square root microcode",
  journal =      j-FORM-METHODS-SYST-DES,
  volume =       "14",
  number =       "1",
  pages =        "75--125",
  month =        jan,
  year =         "1999",
  CODEN =        "FMSDE6",
  ISSN =         "0925-9856 (print), 1572-8102 (electronic)",
  ISSN-L =       "0925-9856",
  bibdate =      "Sat Jun 02 07:51:51 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Special issue on arithmetic circuits.",
  URL =          "http://www.wkap.nl/jrnltoc.htm/0925-9856;
                 http://www.wkap.nl/oasis.htm/194808",
  acknowledgement = ack-nhfb,
  fjournal =     "Formal Methods in System Design",
}


bibtype: article
filename: elefunt.bib
label: Schraudolph:1999:FCA
author: N. N. Schraudolph
title: A Fast, Compact Approximation of the Exponential Function
journal: j-NEURAL-COMP
volume: 11
number: 4
pages: 853--862
day: 1
month: may
monthnumber: 5
year: 1999
CODEN: NEUCEB
DOI: https://doi.org/10.1162/089976699300016467
ISSN: 0899-7667 (print), 1530-888x (electronic) OR 08997667 (print), 1530888x (electronic)
ISSNL: 0899-7667 OR 08997667
bibdate: Fri Nov 8 05:39:32 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; Ingenta database
bibtimestamp: 2002.11.08 05:39:32 MST
URL: https://www.mitpressjournals.org/doi/abs/10.1162/089976699300016467
fjournal: Neural Computation
acknowledgement: ack-nhfb
journalURL: http://www.mitpressjournals.org/loi/neco
rawauthor: N. N. Schraudolph
rawtitle: A Fast, Compact Approximation of the Exponential Function
entry:
@Article{Schraudolph:1999:FCA,
  author =       "N. N. Schraudolph",
  title =        "A Fast, Compact Approximation of the Exponential
                 Function",
  journal =      j-NEURAL-COMP,
  volume =       "11",
  number =       "4",
  pages =        "853--862",
  day =          "1",
  month =        may,
  year =         "1999",
  CODEN =        "NEUCEB",
  DOI =          "https://doi.org/10.1162/089976699300016467",
  ISSN =         "0899-7667 (print), 1530-888x (electronic)",
  ISSN-L =       "0899-7667",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  URL =          "https://www.mitpressjournals.org/doi/abs/10.1162/089976699300016467",
  acknowledgement = ack-nhfb,
  fjournal =     "Neural Computation",
  journal-URL =  "http://www.mitpressjournals.org/loi/neco",
  pagecount =    "10",
}


bibtype: article
filename: elefunt.bib
label: Schulte:1999:AEF
author: M. Schulte and J. Stine
title: Approximating Elementary Functions with Symmetric Bipartite Tables
journal: j-IEEE-TRANS-COMPUT
volume: 48
number: 8
pages: 842--847
year: 1999
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.795125
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Jun 24 20:20:58 2005
bibtimestamp: 2005.06.24 20:20:58 ???
URL: http://mesa.ece.wisc.edu/publications/cp_1999-10.pdf
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. Schulte and J. Stine
rawtitle: Approximating Elementary Functions with Symmetric Bipartite Tables
entry:
@Article{Schulte:1999:AEF,
  author =       "M. Schulte and J. Stine",
  title =        "Approximating Elementary Functions with Symmetric
                 Bipartite Tables",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "8",
  pages =        "842--847",
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.795125",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 24 20:20:58 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-10.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: elefunt.bib
label: Schulte:1999:ESO
author: M. J. Schulte and K. E. Wires
title: Efficient Second Order Approximations for Reciprocals and Square Roots
crossref: Luk:1999:PSA
volume: 3807
pages: 10--18
year: 1999
bibdate: Sun Mar 04 11:10:48 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.03.04 11:10:48 ???
URL: http://mesa.ece.wisc.edu/publications/cp_1999-05.pdf
acknowledgement: ack-nhfb
rawauthor: M. J. Schulte and K. E. Wires
rawtitle: Efficient Second Order Approximations for Reciprocals and Square Roots
entry:
@InProceedings{Schulte:1999:ESO,
  author =       "M. J. Schulte and K. E. Wires",
  title =        "Efficient Second Order Approximations for Reciprocals
                 and Square Roots",
  crossref =     "Luk:1999:PSA",
  volume =       "3807",
  pages =        "10--18",
  year =         "1999",
  bibdate =      "Sun Mar 04 11:10:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-05.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Schulte:1999:HSI
author: Michael J. Schulte and Kent E. Wires
title: High-Speed Inverse Square Roots
crossref: Koren:1999:ISC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 124--131
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
keywords: ARITH; computer arithmetic; IEEE
acknowledgement: ack-nhfb
rawauthor: Michael J. Schulte and Kent E. Wires
rawtitle: High-Speed Inverse Square Roots
URL:
http://euler.ecs.umass.edu/paper/final/paper-109.pdf; http://euler.ecs.umass.edu/paper/final/paper-109.ps

entry:
@InProceedings{Schulte:1999:HSI,
  author =       "Michael J. Schulte and Kent E. Wires",
  title =        "High-Speed Inverse Square Roots",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "124--131",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-109.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-109.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
  summary =      "Inverse square roots are used in several digital
                 signal processing, multimedia, and scientific computing
                 applications. This paper presents a high-speed method
                 for computing inverse square roots. This method uses a
                 table lookup, operand modification, \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Segura:1999:EGT
author: J. Segura and A. Gil
journal: j-COMP-PHYS-COMM
volume: 117
number: 3
pages: 250--262
day: 11
month: mar
monthnumber: 3
year: 1999
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(98)00193-3
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:30:36 MST 2012
bibtimestamp: 2012.02.13 21:30:36 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465598001933
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: J. Segura and A. Gil
title:
ELF and GNOME: Two tiny codes to evaluate the real zeros of the Bessel functions of the first kind for real orders

rawtitle:
{ELF} and {GNOME}: Two tiny codes to evaluate the real zeros of the {Bessel} functions of the first kind for real orders

entry:
@Article{Segura:1999:EGT,
  author =       "J. Segura and A. Gil",
  title =        "{ELF} and {GNOME}: Two tiny codes to evaluate the real
                 zeros of the {Bessel} functions of the first kind for
                 real orders",
  journal =      j-COMP-PHYS-COMM,
  volume =       "117",
  number =       "3",
  pages =        "250--262",
  day =          "11",
  month =        mar,
  year =         "1999",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(98)00193-3",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:36 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465598001933",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Seidel:1999:HSR
author: P.-M. Seidel
title: High-speed redundant reciprocal approximation
journal: j-INTEGRATION-VLSI-J
volume: 28
number: 1
pages: 1--12
month: sep
monthnumber: 9
year: 1999
CODEN: IVJODL
ISSN: 0167-9260 (print), 1872-7522 (electronic) OR 01679260 (print), 18727522 (electronic)
ISSNL: 0167-9260 OR 01679260
bibdate: Fri Nov 8 05:39:32 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; Ingenta database
bibtimestamp: 2002.11.08 05:39:32 MST
fjournal: Integration, the VLSI journal
acknowledgement: ack-nhfb
rawauthor: P.-M. Seidel
rawtitle: High-speed redundant reciprocal approximation
entry:
@Article{Seidel:1999:HSR,
  author =       "P.-M. Seidel",
  title =        "High-speed redundant reciprocal approximation",
  journal =      j-INTEGRATION-VLSI-J,
  volume =       "28",
  number =       "1",
  pages =        "1--12",
  month =        sep,
  year =         "1999",
  CODEN =        "IVJODL",
  ISSN =         "0167-9260 (print), 1872-7522 (electronic)",
  ISSN-L =       "0167-9260",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Integration, the VLSI journal",
  pagecount =    "12",
}


bibtype: article
filename: elefunt.bib
label: Stine:1999:STA
author: E. Stine and M. J. Schulte
title: The Symmetric Table Addition Method for Accurate Function Approximation
journal: j-J-VLSI-SIGNAL-PROC
volume: 21
number: 2
pages: 167--177
month: jun
monthnumber: 6
year: 1999
CODEN: JVSPED
ISSN: 0922-5773 (print), 1573-109x (electronic) OR 09225773 (print), 1573109x (electronic)
ISSNL: 0922-5773 OR 09225773
bibdate: Sun Mar 04 11:02:59 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.03.04 11:02:59 ???
URL: http://mesa.ece.wisc.edu/publications/cp_1999-11.pdf
fjournal: Journal of VLSI Signal Processing
acknowledgement: ack-nhfb
rawauthor: E. Stine and M. J. Schulte
rawtitle: The Symmetric Table Addition Method for Accurate Function Approximation
entry:
@Article{Stine:1999:STA,
  author =       "E. Stine and M. J. Schulte",
  title =        "The Symmetric Table Addition Method for Accurate
                 Function Approximation",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "21",
  number =       "2",
  pages =        "167--177",
  month =        jun,
  year =         "1999",
  CODEN =        "JVSPED",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Sun Mar 04 11:02:59 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-11.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}


bibtype: inproceedings
filename: elefunt.bib
label: Story:1999:NAI
author: S. Story and P. T. P. Tang
title: New Algorithms for Improved Transcendental Functions on IA-64
crossref: Koren:1999:ISC
pages: 4--11
year: 1999
bibdate: Mon Feb 7 07:28:26 MST 2000
bibtimestamp: 2000.02.07 07:28:26 MST
keywords: ARITH; computer arithmetic; IEEE
acknowledgement: ack-nhfb
rawauthor: S. Story and P. T. P. Tang
rawtitle: New Algorithms for Improved Transcendental Functions on {IA-64}
URL:
http://euler.ecs.umass.edu/paper/final/paper-118.pdf; http://euler.ecs.umass.edu/paper/final/paper-118.ps

entry:
@InProceedings{Story:1999:NAI,
  author =       "S. Story and P. T. P. Tang",
  title =        "New Algorithms for Improved Transcendental Functions
                 on {IA-64}",
  crossref =     "Koren:1999:ISC",
  pages =        "4--11",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-118.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-118.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
}


bibtype: book
filename: elefunt.bib
label: Suetin:1999:OPT
author: P. K. (Pavel Kondratevich) Suetin
title: Orthogonal Polynomials in Two Variables
volume: 3
publisher: Gordon and Breach Science Publishers
address: Amsterdam, The Netherlands
pages: xx + 348
year: 1999
ISBN: 90-5699-167-1 OR 9056991671
ISBN13: 978-90-5699-167-8 OR 9789056991678
LCCN: QA404.5 .S8813 1999
bibdate: Sat Oct 30 17:21:54 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:21:54 MDT
note: Translated from the Russian by E. V. Pankratiev.
series: Analytical methods and special functions
remark: Originally published in Russian in 1988 by Nauka, Moscow.
subject: Orthogonal polynomials
acknowledgement: ack-nhfb
rawauthor: P. K. (Pavel Kondratevich) Suetin
rawnote: Translated from the Russian by E. V. Pankratiev.
rawtitle: Orthogonal Polynomials in Two Variables
TOC:
Preface / ix Preface to the English Edition / xv Notation / xix I. General properties of polynomials orthogonal over a domain / 1 1. Polynomials in two variables orthogonal over a domain / 1 2. The existence theorem and criteria of orthogonality / 6 3. Algebraic properties / 10 4. Monic orthogonal polynomials / 18 5. Normal biorthogonal Systems / 24 6. Fourier series of orthogonal polynomials in two variables / 28 7. Fourier series for differentiable functions / 31 II. Some typical examples and special cases of orthogonality over a domain / 37 1. Different products of classical orthogonal polynomials / 37 2. Various cases of connection between orthogonality over a domain and orthogonality on an interval / 42 3. Some theorems in the case of a weight function with separating variables / 48 4. Conditions of interconnection between the weight function and the domain of orthogonality / 52 5. Examples of computations of weight function moments / 57 III. Classical Appell's orthogonal polynomials / 63 1. Rodrigues formula for Appell's polynomials / 63 2. Representation of the Appell polynomials via the hypergeometric function of two variables / 69 3. Differential equation for the Appell polynomials / 72 4. Orthogonality of eigenfunctions of the Appell equation / 75 5. Normal biorthogonal Appell System / 79 6. Series in the Appell polynomials / 83 IV. Admissible differential equation for polynomials orthogonal over a domain / 87 1. The main differential Operator and a theorem on orthogonality / 87 2. Admissibility conditions for the main differential equation / 92 3. Some examples and properties of admissible differential equations / 97 4. Affine transformations of the arguments of the main differential equation / 101 5. Transformation of the coefficients of the characteristic polynomial / 105 6. Normal forms of the admissible differential equation / 115 7. Normal forms when reducing the degree of the characteristic polynomial / 123 V. Potentially self-adjoint equation and Rodrigues formula / 131 1. Potentially self-adjoint Operators / 131 2. Admissible and potentially self-adjoint equations / 135 3. Rodrigues formula for polynomials orthogonal over a domain / 146 4. Weight functions and the Rodrigues formula in the most typical cases / 153 VI. Harmonic polynomials orthogonal over a domain / 163 1. Homogeneous harmonic polynomials / 163 2. An analogue of the Christoffel--Darboux formula / 169 3. Harmonic polynomials orthogonal in the unit disk / 173 4. Harmonic polynomials orthogonal over a domain in the general case / 176 5. Harmonic polynomials superorthogonal over a domain / 179 VII. Polynomials in two variables orthogonal on a contour / 187 1. Main definitions and the simplest properties / 187 2. Polynomials in two variables orthogonal on an algebraic curve / 191 3. Harmonic polynomials orthogonal on a contour / 196 4. Fourier series in harmonic polynomials orthogonal on a contour / 200 5. Harmonic polynomials superorthogonal on a contour / 206 6. Examples of superorthogonal Systems of harmonic polynomials / 213 VIII. Generalized orthogonal polynomials in two variables / 223 1. Main definitions and the simplest properties / 223 2. The existence theorem in the most general form / 228 3. Fourier series in generalized orthogonal polynomials in two variables / 233 4. Monic orthogonal polynomials under minimal conditions / 241 5. Generalized generating functions for monic orthogonal polynomials / 247 IX. Other results concerning the connection between orthogonal polynomials and differential equations / 253 1. Canonical admissible differential equation and monic orthogonal polynomials / 253 2. Necessary consistency conditions of the canonical Operator and the functional / 258 3. Sufficient conditions of consistency of the canonical Operator and the functional / 262 4. The deduction of the differential equation from the Pearson equation System / 268 5. An admissible partial differential equation of an arbitrary order / 276 X. Original results of T. Koornwinder / 285 1. Examples of the representation of polynomials orthogonal over a domain via the Jacobi polynomials / 285 2. Orthogonal polynomials in two conjugate complex variables / 291 3. The Chebyshev polynomials in two conjugate complex variables for the Steiner domain / 296 4. Another generalization of the Jacobi polynomials onto the case of two variables / 308 XI. Some recent results / 313 1. A new generalization of the Appell polynomials / 313 2. Some properties of the Koornwinder--Steiner polynomials / 318 3. A two-dimensional analogue of the Chebyshev--Laguerre polynomials / 319 Comments and Supplements / 323 References / 329 Author Index / 343 Subject Index / 345

rawTOC:
Preface / ix \\ Preface to the English Edition / xv \\ Notation / xix \\ I. General properties of polynomials orthogonal over a domain / 1 \\ 1. Polynomials in two variables orthogonal over a domain / 1 \\ 2. The existence theorem and criteria of orthogonality / 6 \\ 3. Algebraic properties / 10 \\ 4. Monic orthogonal polynomials / 18 \\ 5. Normal biorthogonal Systems / 24 \\ 6. Fourier series of orthogonal polynomials in two variables / 28 \\ 7. Fourier series for differentiable functions / 31 \\ II. Some typical examples and special cases of orthogonality over a domain / 37 \\ 1. Different products of classical orthogonal polynomials / 37 \\ 2. Various cases of connection between orthogonality over a domain and orthogonality on an interval / 42 \\ 3. Some theorems in the case of a weight function with separating variables / 48 \\ 4. Conditions of interconnection between the weight function and the domain of orthogonality / 52 \\ 5. Examples of computations of weight function moments / 57 \\ III. Classical Appell's orthogonal polynomials / 63 \\ 1. Rodrigues formula for Appell's polynomials / 63 \\ 2. Representation of the Appell polynomials via the hypergeometric function of two variables / 69 \\ 3. Differential equation for the Appell polynomials / 72 \\ 4. Orthogonality of eigenfunctions of the Appell equation / 75 \\ 5. Normal biorthogonal Appell System / 79 \\ 6. Series in the Appell polynomials / 83 \\ IV. Admissible differential equation for polynomials orthogonal over a domain / 87 \\ 1. The main differential Operator and a theorem on orthogonality / 87 \\ 2. Admissibility conditions for the main differential equation / 92 \\ 3. Some examples and properties of admissible differential equations / 97 \\ 4. Affine transformations of the arguments of the main differential equation / 101 \\ 5. Transformation of the coefficients of the characteristic polynomial / 105 \\ 6. Normal forms of the admissible differential equation / 115 \\ 7. Normal forms when reducing the degree of the characteristic polynomial / 123 \\ V. Potentially self-adjoint equation and Rodrigues formula / 131 \\ 1. Potentially self-adjoint Operators / 131 \\ 2. Admissible and potentially self-adjoint equations / 135 \\ 3. Rodrigues formula for polynomials orthogonal over a domain / 146 \\ 4. Weight functions and the Rodrigues formula in the most typical cases / 153 \\ VI. Harmonic polynomials orthogonal over a domain / 163 \\ 1. Homogeneous harmonic polynomials / 163 \\ 2. An analogue of the Christoffel--Darboux formula / 169 \\ 3. Harmonic polynomials orthogonal in the unit disk / 173 \\ 4. Harmonic polynomials orthogonal over a domain in the general case / 176 \\ 5. Harmonic polynomials superorthogonal over a domain / 179 \\ VII. Polynomials in two variables orthogonal on a contour / 187 \\ 1. Main definitions and the simplest properties / 187 \\ 2. Polynomials in two variables orthogonal on an algebraic curve / 191 \\ 3. Harmonic polynomials orthogonal on a contour / 196 \\ 4. Fourier series in harmonic polynomials orthogonal on a contour / 200 \\ 5. Harmonic polynomials superorthogonal on a contour / 206 \\ 6. Examples of superorthogonal Systems of harmonic polynomials / 213 \\ VIII. Generalized orthogonal polynomials in two variables / 223 \\ 1. Main definitions and the simplest properties / 223 \\ 2. The existence theorem in the most general form / 228 \\ 3. Fourier series in generalized orthogonal polynomials in two variables / 233 \\ 4. Monic orthogonal polynomials under minimal conditions / 241 \\ 5. Generalized generating functions for monic orthogonal polynomials / 247 \\ IX. Other results concerning the connection between orthogonal polynomials and differential equations / 253 \\ 1. Canonical admissible differential equation and monic orthogonal polynomials / 253 \\ 2. Necessary consistency conditions of the canonical Operator and the functional / 258 \\ 3. Sufficient conditions of consistency of the canonical Operator and the functional / 262 \\ 4. The deduction of the differential equation from the Pearson equation System / 268 \\ 5. An admissible partial differential equation of an arbitrary order / 276 \\ X. Original results of T. Koornwinder / 285 \\ 1. Examples of the representation of polynomials orthogonal over a domain via the Jacobi polynomials / 285 \\ 2. Orthogonal polynomials in two conjugate complex variables / 291 \\ 3. The Chebyshev polynomials in two conjugate complex variables for the Steiner domain / 296 \\ 4. Another generalization of the Jacobi polynomials onto the case of two variables / 308 \\ XI. Some recent results / 313 \\ 1. A new generalization of the Appell polynomials / 313 \\ 2. Some properties of the Koornwinder--Steiner polynomials / 318 \\ 3. A two-dimensional analogue of the Chebyshev--Laguerre polynomials / 319 \\ Comments and Supplements / 323 \\ References / 329 \\ Author Index / 343 \\ Subject Index / 345

entry:
@Book{Suetin:1999:OPT,
  author =       "P. K. (Pavel Kondratevich) Suetin",
  title =        "Orthogonal Polynomials in Two Variables",
  volume =       "3",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "Amsterdam, The Netherlands",
  pages =        "xx + 348",
  year =         "1999",
  ISBN =         "90-5699-167-1",
  ISBN-13 =      "978-90-5699-167-8",
  LCCN =         "QA404.5 .S8813 1999",
  bibdate =      "Sat Oct 30 17:21:54 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  note =         "Translated from the Russian by E. V. Pankratiev.",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  remark =       "Originally published in Russian in 1988 by Nauka,
                 Moscow.",
  subject =      "Orthogonal polynomials",
  tableofcontents = "Preface / ix \\
                 Preface to the English Edition / xv \\
                 Notation / xix \\
                 I. General properties of polynomials orthogonal over a
                 domain / 1 \\
                 1. Polynomials in two variables orthogonal over a
                 domain / 1 \\
                 2. The existence theorem and criteria of orthogonality
                 / 6 \\
                 3. Algebraic properties / 10 \\
                 4. Monic orthogonal polynomials / 18 \\
                 5. Normal biorthogonal Systems / 24 \\
                 6. Fourier series of orthogonal polynomials in two
                 variables / 28 \\
                 7. Fourier series for differentiable functions / 31 \\
                 II. Some typical examples and special cases of
                 orthogonality over a domain / 37 \\
                 1. Different products of classical orthogonal
                 polynomials / 37 \\
                 2. Various cases of connection between orthogonality
                 over a domain and orthogonality on an interval / 42 \\
                 3. Some theorems in the case of a weight function with
                 separating variables / 48 \\
                 4. Conditions of interconnection between the weight
                 function and the domain of orthogonality / 52 \\
                 5. Examples of computations of weight function moments
                 / 57 \\
                 III. Classical Appell's orthogonal polynomials / 63 \\
                 1. Rodrigues formula for Appell's polynomials / 63 \\
                 2. Representation of the Appell polynomials via the
                 hypergeometric function of two variables / 69 \\
                 3. Differential equation for the Appell polynomials /
                 72 \\
                 4. Orthogonality of eigenfunctions of the Appell
                 equation / 75 \\
                 5. Normal biorthogonal Appell System / 79 \\
                 6. Series in the Appell polynomials / 83 \\
                 IV. Admissible differential equation for polynomials
                 orthogonal over a domain / 87 \\
                 1. The main differential Operator and a theorem on
                 orthogonality / 87 \\
                 2. Admissibility conditions for the main differential
                 equation / 92 \\
                 3. Some examples and properties of admissible
                 differential equations / 97 \\
                 4. Affine transformations of the arguments of the main
                 differential equation / 101 \\
                 5. Transformation of the coefficients of the
                 characteristic polynomial / 105 \\
                 6. Normal forms of the admissible differential equation
                 / 115 \\
                 7. Normal forms when reducing the degree of the
                 characteristic polynomial / 123 \\
                 V. Potentially self-adjoint equation and Rodrigues
                 formula / 131 \\
                 1. Potentially self-adjoint Operators / 131 \\
                 2. Admissible and potentially self-adjoint equations /
                 135 \\
                 3. Rodrigues formula for polynomials orthogonal over a
                 domain / 146 \\
                 4. Weight functions and the Rodrigues formula in the
                 most typical cases / 153 \\
                 VI. Harmonic polynomials orthogonal over a domain / 163
                 \\
                 1. Homogeneous harmonic polynomials / 163 \\
                 2. An analogue of the Christoffel--Darboux formula /
                 169 \\
                 3. Harmonic polynomials orthogonal in the unit disk /
                 173 \\
                 4. Harmonic polynomials orthogonal over a domain in the
                 general case / 176 \\
                 5. Harmonic polynomials superorthogonal over a domain /
                 179 \\
                 VII. Polynomials in two variables orthogonal on a
                 contour / 187 \\
                 1. Main definitions and the simplest properties / 187
                 \\
                 2. Polynomials in two variables orthogonal on an
                 algebraic curve / 191 \\
                 3. Harmonic polynomials orthogonal on a contour / 196
                 \\
                 4. Fourier series in harmonic polynomials orthogonal on
                 a contour / 200 \\
                 5. Harmonic polynomials superorthogonal on a contour /
                 206 \\
                 6. Examples of superorthogonal Systems of harmonic
                 polynomials / 213 \\
                 VIII. Generalized orthogonal polynomials in two
                 variables / 223 \\
                 1. Main definitions and the simplest properties / 223
                 \\
                 2. The existence theorem in the most general form / 228
                 \\
                 3. Fourier series in generalized orthogonal polynomials
                 in two variables / 233 \\
                 4. Monic orthogonal polynomials under minimal
                 conditions / 241 \\
                 5. Generalized generating functions for monic
                 orthogonal polynomials / 247 \\
                 IX. Other results concerning the connection between
                 orthogonal polynomials and differential equations / 253
                 \\
                 1. Canonical admissible differential equation and monic
                 orthogonal polynomials / 253 \\
                 2. Necessary consistency conditions of the canonical
                 Operator and the functional / 258 \\
                 3. Sufficient conditions of consistency of the
                 canonical Operator and the functional / 262 \\
                 4. The deduction of the differential equation from the
                 Pearson equation System / 268 \\
                 5. An admissible partial differential equation of an
                 arbitrary order / 276 \\
                 X. Original results of T. Koornwinder / 285 \\
                 1. Examples of the representation of polynomials
                 orthogonal over a domain via the Jacobi polynomials /
                 285 \\
                 2. Orthogonal polynomials in two conjugate complex
                 variables / 291 \\
                 3. The Chebyshev polynomials in two conjugate complex
                 variables for the Steiner domain / 296 \\
                 4. Another generalization of the Jacobi polynomials
                 onto the case of two variables / 308 \\
                 XI. Some recent results / 313 \\
                 1. A new generalization of the Appell polynomials / 313
                 \\
                 2. Some properties of the Koornwinder--Steiner
                 polynomials / 318 \\
                 3. A two-dimensional analogue of the
                 Chebyshev--Laguerre polynomials / 319 \\
                 Comments and Supplements / 323 \\
                 References / 329 \\
                 Author Index / 343 \\
                 Subject Index / 345",
}


bibtype: article
filename: elefunt.bib
label: Vrahatis:1999:ESP
author: M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A. Zafiropoulos and T. N. Grapsa
journal: j-COMP-PHYS-COMM
volume: 117
number: 3
pages: 290--290
day: 11
month: mar
monthnumber: 3
year: 1999
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(98)00109-X
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:30:36 MST 2012
bibtimestamp: 2012.02.13 21:30:36 MST
note: See cite Vrahatis:1995:RPP.
URL: http://www.sciencedirect.com/science/article/pii/S001046559800109X
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A. Zafiropoulos and T. N. Grapsa
rawnote: See \cite{Vrahatis:1995:RPP}.
title:
Erratum to: booktitle RFSFNS: a portable package for the numerical determination of the number and the calculation of roots of Bessel functions [Comput. Phys. Commun. bf 92 (1995) 252--266]

rawtitle:
Erratum to: {{\booktitle{RFSFNS: a portable package for the numerical determination of the number and the calculation of roots of Bessel functions}} [Comput. Phys. Commun. {\bf 92} (1995) 252--266]}

entry:
@Article{Vrahatis:1999:ESP,
  author =       "M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A.
                 Zafiropoulos and T. N. Grapsa",
  title =        "Erratum to: {{\booktitle{RFSFNS: a portable package
                 for the numerical determination of the number and the
                 calculation of roots of Bessel functions}} [Comput.
                 Phys. Commun. {\bf 92} (1995) 252--266]}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "117",
  number =       "3",
  pages =        "290--290",
  day =          "11",
  month =        mar,
  year =         "1999",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(98)00109-X",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:36 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Vrahatis:1995:RPP}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S001046559800109X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Vyridis:1999:ICA
author: D. G. Vyridis and S. D. Panteliou and I. N. Katz
title: An inverse convergence approach for arguments of Jacobian elliptic functions
journal: j-COMPUT-MATH-APPL
volume: 37
number: 2
pages: 21--26
month: jan
monthnumber: 1
year: 1999
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:56 MST 2017
bibtimestamp: 2017.03.01 21:48:56 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122198002508
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: D. G. Vyridis and S. D. Panteliou and I. N. Katz
rawtitle: An inverse convergence approach for arguments of {Jacobian} elliptic functions
entry:
@Article{Vyridis:1999:ICA,
  author =       "D. G. Vyridis and S. D. Panteliou and I. N. Katz",
  title =        "An inverse convergence approach for arguments of
                 {Jacobian} elliptic functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "37",
  number =       "2",
  pages =        "21--26",
  month =        jan,
  year =         "1999",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:56 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122198002508",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Wieder:1999:ANH
author: Thomas Wieder
title: Algorithm 794: Numerical Hankel transform by the Fortran program HANKEL
journal: j-TOMS
volume: 25
number: 2
pages: 240--250
month: jun
monthnumber: 6
year: 1999
CODEN: ACMSCU
DOI: https://doi.org/10.1145/317275.317284
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Oct 20 18:21:35 MDT 1999
bibsource: http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.20 18:21:35 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: Hankel transform; numerical analysis
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Thomas Wieder
rawtitle: {Algorithm 794}: Numerical {Hankel} transform by the {Fortran} program {HANKEL}
URL:
ftp://netlib.bell-labs.com/netlib/toms/794.gz; http://phase.etl.go.jp/netlib/toms/794; http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p240-wieder/; http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Wieder:1999:ANH; http://www.hensa.ac.uk/netlib/toms/794.gz; http://www.netlib.no/netlib/toms/794; http://www.netlib.org/toms/794

abstract:
The numerical evaluation of the Hankel transform poses the problems of both infinite integration and Bessel function calculation. Using the corresponding numerical program routines from the literature, a Fortran program has been written to perform the Hankel transform for real functions, given either in analytical form as subroutines or in discrete form as tabulated data.

subject:
Software --- Programming Languages --- Language Classifications (D.3.2): FORTRAN 77; Theory of Computation --- Analysis of Algorithms and Problem Complexity --- Numerical Algorithms and Problems (F.2.1): Computation of transforms

rawabstract:
The numerical evaluation of the Hankel transform poses the problems of both infinite integration and Bessel function calculation. Using the corresponding numerical program routines from the literature, a Fortran program has been written to perform the Hankel transform for real functions, given either in analytical form as subroutines or in discrete form as tabulated data.

entry:
@Article{Wieder:1999:ANH,
  author =       "Thomas Wieder",
  title =        "{Algorithm 794}: Numerical {Hankel} transform by the
                 {Fortran} program {HANKEL}",
  journal =      j-TOMS,
  volume =       "25",
  number =       "2",
  pages =        "240--250",
  month =        jun,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/317275.317284",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 20 18:21:35 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "ftp://netlib.bell-labs.com/netlib/toms/794.gz;
                 http://phase.etl.go.jp/netlib/toms/794;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p240-wieder/;
                 http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Wieder:1999:ANH;
                 http://www.hensa.ac.uk/netlib/toms/794.gz;
                 http://www.netlib.no/netlib/toms/794;
                 http://www.netlib.org/toms/794",
  abstract =     "The numerical evaluation of the Hankel transform poses
                 the problems of both infinite integration and Bessel
                 function calculation. Using the corresponding numerical
                 program routines from the literature, a Fortran program
                 has been written to perform the Hankel transform for
                 real functions, given either in analytical form as
                 subroutines or in discrete form as tabulated data.",
  accepted =     "February 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Hankel transform; numerical analysis",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): FORTRAN 77; Theory of
                 Computation --- Analysis of Algorithms and Problem
                 Complexity --- Numerical Algorithms and Problems
                 (F.2.1): Computation of transforms",
}


bibtype: techreport
filename: elefunt.bib
label: Zimmermann:1999:KSR
author: Paul Zimmermann
title: Karatsuba Square Root
type: Research Report
number: 3805
institution: inst-LORIA-INRIA-LORRAINE
address: inst-LORIA-INRIA-LORRAINE:adr
pages: 8
year: 1999
bibdate: Sun Sep 10 08:56:48 2006
bibtimestamp: 2006.09.10 08:56:48 ???
acknowledgement: ack-nhfb
rawauthor: Paul Zimmermann
rawtitle: {Karatsuba} Square Root
URL:
ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-3805.pdf; ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-3805.ps.gz; http://www.inria.fr/rrrt/rr-3805.html

abstract:
We exhibit an algorithm to compute the square-root with remainder of a $n$-word number in $ 3 / 2 $ word operations, where $ K(n) $ is the number of words operations to multiply two $n$-word numbers using Karatsuba's algorithm. If the remainder is not needed, the cost can be reduced to $ K(n) $ on average. This algorithm can be used for floating-point or polynomial computations too; although not optimal asymptotically, its simplicity gives a wide range of use, from about 50 to 1,000,000 digits, as shown by computer experiments.

rawabstract:
We exhibit an algorithm to compute the square-root with remainder of a $n$-word number in $ 3 / 2 $ word operations, where $ K(n) $ is the number of words operations to multiply two $n$-word numbers using Karatsuba's algorithm. If the remainder is not needed, the cost can be reduced to $ K(n) $ on average. This algorithm can be used for floating-point or polynomial computations too; although not optimal asymptotically, its simplicity gives a wide range of use, from about 50 to 1,000,000 digits, as shown by computer experiments.

entry:
@TechReport{Zimmermann:1999:KSR,
  author =       "Paul Zimmermann",
  title =        "{Karatsuba} Square Root",
  type =         "Research Report",
  number =       "3805",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "8",
  year =         "1999",
  bibdate =      "Sun Sep 10 08:56:48 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-3805.pdf;
                 ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-3805.ps.gz;
                 http://www.inria.fr/rrrt/rr-3805.html",
  abstract =     "We exhibit an algorithm to compute the square-root
                 with remainder of a $n$-word number in $ 3 / 2 $ word
                 operations, where $ K(n) $ is the number of words
                 operations to multiply two $n$-word numbers using
                 Karatsuba's algorithm. If the remainder is not needed,
                 the cost can be reduced to $ K(n) $ on average. This
                 algorithm can be used for floating-point or polynomial
                 computations too; although not optimal asymptotically,
                 its simplicity gives a wide range of use, from about 50
                 to 1,000,000 digits, as shown by computer
                 experiments.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Ziv:1999:SUR
author: Abraham Ziv
title: Sharp ULP rounding error bound for the hypotenuse function
journal: j-MATH-COMPUT
volume: 68
number: 227
pages: 1143--1148
month: jul
monthnumber: 7
year: 1999
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Fri Jul 16 10:39:05 MDT 1999
bibtimestamp: 1999.07.16 10:39:05 MDT
URL: http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-99-01103-5&u=/mcom/1999-68-227/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: Abraham Ziv
rawtitle: Sharp {ULP} rounding error bound for the hypotenuse function
bibsource:
http://www.ams.org/mcom/1999-68-227; 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/mathcomp1990.bib

entry:
@Article{Ziv:1999:SUR,
  author =       "Abraham Ziv",
  title =        "Sharp {ULP} rounding error bound for the hypotenuse
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "68",
  number =       "227",
  pages =        "1143--1148",
  month =        jul,
  year =         "1999",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Fri Jul 16 10:39:05 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1999-68-227;
                 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/mathcomp1990.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-99-01103-5&u=/mcom/1999-68-227/",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Alhargan:2000:ACA
author: Fayez A. Alhargan
title: Algorithms for the Computation of all Mathieu Functions of Integer Orders
journal: j-TOMS
volume: 26
number: 3
pages: 390--407
month: sep
monthnumber: 9
year: 2000
CODEN: ACMSCU
DOI: https://doi.org/10.1145/358407.358420
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Feb 6 16:43:42 MST 2002
bibtimestamp: 2002.02.06 16:43:42 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Fayez A. Alhargan
rawtitle: Algorithms for the Computation of all {Mathieu} Functions of Integer Orders
bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
The paper presents methods for the computation of all Mathieu functions of integer order, which cover a large range of $n$ and $h$; previous algorithms were limited to small values of $n$. The algorithms are given in sufficient details to enable straightforward implementation. The algorithms can handle a large range of the order $n$ (0-200) and the parameter $h$ (0-4$n$ ).

rawabstract:
The paper presents methods for the computation of all Mathieu functions of integer order, which cover a large range of $n$ and $h$; previous algorithms were limited to small values of $n$. The algorithms are given in sufficient details to enable straightforward implementation. The algorithms can handle a large range of the order $n$ (0-200) and the parameter $h$ (0-4$n$ ).

entry:
@Article{Alhargan:2000:ACA,
  author =       "Fayez A. Alhargan",
  title =        "Algorithms for the Computation of all {Mathieu}
                 Functions of Integer Orders",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "390--407",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358420",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The paper presents methods for the computation of all
                 Mathieu functions of integer order, which cover a large
                 range of $n$ and $h$; previous algorithms were limited
                 to small values of $n$. The algorithms are given in
                 sufficient details to enable straightforward
                 implementation. The algorithms can handle a large range
                 of the order $n$ (0-200) and the parameter $h$ (0-4$n$
                 ).",
  accepted =     "19 May 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Alhargan:2000:ASC
author: Fayez A. Alhargan
title: Algorithm 804: subroutines for the computation of Mathieu functions of integer orders
journal: j-TOMS
volume: 26
number: 3
pages: 408--414
month: sep
monthnumber: 9
year: 2000
CODEN: ACMSCU
DOI: https://doi.org/10.1145/358407.358422
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Feb 6 16:43:42 MST 2002
bibtimestamp: 2002.02.06 16:43:42 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Fayez A. Alhargan
rawtitle: {Algorithm 804}: subroutines for the computation of {Mathieu} functions of integer orders
bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
Computer subroutines in C++ for computing Mathieu functions of integer orders are described. The core routines for computing Mathieu characteristic numbers and Mathieu coefficients are described in details, the rest of the subroutines are standard implementation of the series summations for each function. The routines can handle a large range of the order $n$ and the parameter $h$.

rawabstract:
Computer subroutines in C++ for computing Mathieu functions of integer orders are described. The core routines for computing Mathieu characteristic numbers and Mathieu coefficients are described in details, the rest of the subroutines are standard implementation of the series summations for each function. The routines can handle a large range of the order $n$ and the parameter $h$.

entry:
@Article{Alhargan:2000:ASC,
  author =       "Fayez A. Alhargan",
  title =        "{Algorithm 804}: subroutines for the computation of
                 {Mathieu} functions of integer orders",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "408--414",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358422",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Computer subroutines in C++ for computing Mathieu
                 functions of integer orders are described. The core
                 routines for computing Mathieu characteristic numbers
                 and Mathieu coefficients are described in details, the
                 rest of the subroutines are standard implementation of
                 the series summations for each function. The routines
                 can handle a large range of the order $n$ and the
                 parameter $h$.",
  accepted =     "19 May 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Anderson:2000:RAF
author: Stuart Anderson
title: Remark on Algorithm 723: Fresnel integrals
journal: j-TOMS
volume: 26
number: 4
pages: 617--617
month: dec
monthnumber: 12
year: 2000
CODEN: ACMSCU
DOI: https://doi.org/10.1145/365723.365737
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Feb 6 16:43:42 MST 2002
bibtimestamp: 2002.02.06 16:43:42 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Stuart Anderson
rawtitle: Remark on {Algorithm 723}: {Fresnel} integrals
entry:
@Article{Anderson:2000:RAF,
  author =       "Stuart Anderson",
  title =        "Remark on {Algorithm 723}: {Fresnel} integrals",
  journal =      j-TOMS,
  volume =       "26",
  number =       "4",
  pages =        "617--617",
  month =        dec,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/365723.365737",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  accepted =     "16 October 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Ball:2000:ACZ
author: James S. Ball
title: Automatic Computation of Zeros of Bessel Functions and Other Special Functions
journal: j-SIAM-J-SCI-COMP
volume: 21
number: 4
pages: 1458--1464
month: jul
monthnumber: 7
year: 2000
CODEN: SJOCE3
DOI: https://doi.org/10.1137/S1064827598339074
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
bibdate: Fri Oct 27 13:32:22 MDT 2000
bibtimestamp: 2000.10.27 13:32:22 MDT
URL: http://epubs.siam.org/sam-bin/dbq/article/33907
fjournal: SIAM Journal on Scientific Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sisc
rawauthor: James S. Ball
rawtitle: Automatic Computation of Zeros of {Bessel} Functions and Other Special Functions
bibsource:
http://epubs.siam.org/toc/sjoce3/21/4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib

entry:
@Article{Ball:2000:ACZ,
  author =       "James S. Ball",
  title =        "Automatic Computation of Zeros of {Bessel} Functions
                 and Other Special Functions",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "21",
  number =       "4",
  pages =        "1458--1464",
  month =        jul,
  year =         "2000",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827598339074",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Oct 27 13:32:22 MDT 2000",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/21/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/33907",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}


bibtype: article
filename: elefunt.bib
label: Barry:2000:AAR
author: D. A. Barry and J.-Y Parlange and L. Li and H. Prommer and C. J. Cunningham and F. Stagnitti
title: Analytical approximations for real values of the Lambert $W$-function
journal: j-MATH-COMPUT-SIMUL
volume: 53
number: 1--2
pages: 95--103
day: 15
month: aug
monthnumber: 8
year: 2000
CODEN: MCSIDR
DOI: https://doi.org/10.1016/S0378-4754(00)00172-5
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
bibdate: Sat Aug 16 16:59:35 MDT 2025
bibtimestamp: 2025.08.16 16:59:35 MDT
URL: https://www.sciencedirect.com/science/article/pii/S0378475400001725
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
ajournal: Math. Comput. Simul.
journalURL: https://www.sciencedirect.com/science/journal/03784754
rawauthor: D. A. Barry and J.-Y Parlange and L. Li and H. Prommer and C. J. Cunningham and F. Stagnitti
rawtitle: Analytical approximations for real values of the {Lambert} {$W$}-function
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomputsimul2000.bib

entry:
@Article{Barry:2000:AAR,
  author =       "D. A. Barry and J.-Y Parlange and L. Li and H. Prommer
                 and C. J. Cunningham and F. Stagnitti",
  title =        "Analytical approximations for real values of the
                 {Lambert} {$W$}-function",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "53",
  number =       "1--2",
  pages =        "95--103",
  day =          "15",
  month =        aug,
  year =         "2000",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/S0378-4754(00)00172-5",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Sat Aug 16 16:59:35 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul2000.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0378475400001725",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}


bibtype: inproceedings
filename: elefunt.bib
label: Batten:2000:NAD
author: D. Batten and S. Jinturkar and J. Glossner and M. Schulte and P. D'arcy
title: A New Approach to DSP Intrinsic Functions
crossref: Sprague:2000:PAH
pages: 2892--2901
year: 2000
bibdate: Sun Mar 04 11:18:38 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.03.04 11:18:38 ???
URL: http://mesa.ece.wisc.edu/publications/cp_2000-01.pdf
acknowledgement: ack-nhfb
rawauthor: D. Batten and S. Jinturkar and J. Glossner and M. Schulte and P. D'arcy
rawtitle: A New Approach to {DSP} Intrinsic Functions
entry:
@InProceedings{Batten:2000:NAD,
  author =       "D. Batten and S. Jinturkar and J. Glossner and M.
                 Schulte and P. D'arcy",
  title =        "A New Approach to {DSP} Intrinsic Functions",
  crossref =     "Sprague:2000:PAH",
  pages =        "2892--2901",
  year =         "2000",
  bibdate =      "Sun Mar 04 11:18:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-01.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Becken:2000:ACG
author: W. Becken and P. Schmelcher
journal: j-J-COMPUT-APPL-MATH
volume: 126
number: 1--2
pages: 449--478
day: 30
month: dec
monthnumber: 12
year: 2000
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(00)00267-3
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 33C05 (33F05)
MRnumber: MR1806771 (2002e:33003)
bibdate: Sat Feb 25 12:43:38 MST 2017
bibtimestamp: 2017.02.25 12:43:38 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700002673
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: W. Becken and P. Schmelcher
title:
The analytic continuation of the Gaussian hypergeometric function $_2 F_1 (a, b; c; z)$ for arbitrary parameters

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib

rawtitle:
The analytic continuation of the {Gaussian} hypergeometric function {$_2 F_1 (a, b; c; z)$} for arbitrary parameters

entry:
@Article{Becken:2000:ACG,
  author =       "W. Becken and P. Schmelcher",
  title =        "The analytic continuation of the {Gaussian}
                 hypergeometric function {$_2 F_1 (a, b; c; z)$} for
                 arbitrary parameters",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "126",
  number =       "1--2",
  pages =        "449--478",
  day =          "30",
  month =        dec,
  year =         "2000",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00267-3",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "33C05 (33F05)",
  MRnumber =     "MR1806771 (2002e:33003)",
  bibdate =      "Sat Feb 25 12:43:38 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700002673",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: incollection
filename: elefunt.bib
label: 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
bibtimestamp: 2016.08.11 09:36:22 MDT
note: Reprint of cite Borwein:1984:AGM.
URL: http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_56
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein
rawnote: Reprint of \cite{Borwein:1984:AGM}.
rawtitle: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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

entry:
@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",
}


bibtype: article
filename: elefunt.bib
label: Borwein:2000:CSR
author: Jonathan M. Borwein and David M. Bradley and Richard E. Crandall
title: Computational Strategies for the Riemann Zeta Function
journal: j-J-COMPUT-APPL-MATH
volume: 121
number: 1--2
pages: 247--296
month: sep
monthnumber: 9
year: 2000
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(00)00336-8
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 11M06 (11Y35 33F05)
MRnumber: 1780051
MRreviewer: Cem Y. Y{\i}ld{\i}r{\i}m
bibdate: Mon Oct 24 11:41:28 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.10.24 11:41:28 ???
URL: http://people.reed.edu/~crandall/papers/attach01.pdf
fjournal: Journal of Computational and Applied Mathematics
remark: CECM Preprint 98:118.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Jonathan M. Borwein and David M. Bradley and Richard E. Crandall
rawtitle: Computational Strategies for the {Riemann} Zeta Function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the incidence of what we call ``value recycling''.

rawabstract:
We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the incidence of what we call ``value recycling''.

entry:
@Article{Borwein:2000:CSR,
  author =       "Jonathan M. Borwein and David M. Bradley and Richard
                 E. Crandall",
  title =        "Computational Strategies for the {Riemann} Zeta
                 Function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "121",
  number =       "1--2",
  pages =        "247--296",
  month =        sep,
  year =         "2000",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00336-8",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "11M06 (11Y35 33F05)",
  MRnumber =     "1780051",
  MRreviewer =   "Cem Y. Y{\i}ld{\i}r{\i}m",
  bibdate =      "Mon Oct 24 11:41:28 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://people.reed.edu/~crandall/papers/attach01.pdf",
  abstract =     "We provide a compendium of evaluation methods for the
                 Riemann zeta function, presenting formulae ranging from
                 historical attempts to recently found convergent series
                 to curious oddities old and new. We concentrate
                 primarily on practical computational issues, such
                 issues depending on the domain of the argument, the
                 desired speed of computation, and the incidence of what
                 we call ``value recycling''.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 98:118.",
}


bibtype: book
filename: elefunt.bib
label: Bressoud:2000:CCN
author: David M. Bressoud and S. Wagon
title: A Course in Computational Number Theory
publisher: Key College Publishers in cooperation with Springer
address: New York, NY, USA
pages: xii + 367
year: 2000
ISBN: 1-930190-10-7 OR 1930190107
ISBN13: 978-1-930190-10-8 OR 9781930190108
LCCN: QA241 .B788 2000
bibdate: Fri Sep 26 14:29:31 MDT 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2008.09.26 14:29:31 MDT
subject: Number theory; Algorithms
acknowledgement: ack-nhfb
rawauthor: David M. Bressoud and S. Wagon
rawtitle: A Course in Computational Number Theory
URL:
http://www.loc.gov/catdir/enhancements/fy0818/99016037-d.html; http://www.loc.gov/catdir/enhancements/fy0818/99016037-t.html

TOC:
Preface Vv Notation Xi Chapter 1. Fundamentals / 1 1.0 Introduction / 1 1.1 A Famous Sequence of Numbers / 2 1.2 The Euclidean Algorithm / 6 The Oldest Algorithm Reversing the Euclidean Algorithm The Extended GCD Algorithm The Fundamental Theorem of Arithmetic Two Applications 1.3 Modular Arithmetic / 25 1.4 Fast Powers / 30 A Fast Algorithm for Exponentiation Powers of Matrices, Big-O Notation Chapter 2. Congruences, Equations, and Powers / 41 2.0 Introduction / / 41 2.1 Solving Linear Congruences / 41 Linear Diophantine Equations in Two Variables Linear Equations in Several Variables Linear Congruences The Conductor An Important Quadratic Congruence 2.2 The Chinese Remainder Theorem / 49 2.3 PowerMod Patterns / 55 Fermat's Little Theorem More Patterns in Powers 2.4 Pseudoprimes / 59 Using the Pseudoprime Test Chapter 3. Euler's $phi $ Function / 65 3.0 Introduction / 65 3.1 Euler's $phi $ Function / 656 3.2 Perfect Numbers and Their Relatives / 12 The Sum of Divisors Function Perfect Numbers Amicable, Abundant, and Deficient Numbers 3.3 Euler's Theorem / 81 3.4 Primitive Roots for Primes / 84 The Order of an Integer Primes Have Primitive Roots Repeating Decimals 3.5 Primitive Roots for Composites / 70 3.6 The Universal Exponent / 73 Universal Exponents Power Towers The Form of Carmichael Numbers Chapter 4. Prime Numbers / 99 4.0 Introduction / 99 4.1 The number of Primes / 100 We'll Never Run Out of Primes The Sieve of Eratosthenes Chebyshev's Theorem and Bertrand's Postulate 4.2 Prime Testing and Certification / 114 Strong Pseudoprimes Industrial-Grade Primes Prime Certification Via Primitive Roots An Improvement Pratt Certificates 4.3 Refinements and Other Directions / 131 Other Primality Tests Strong Liars Are Scarce Finding the $n$th Prime 4.4 A Dozen Prime Mysteries / 141 5.0 Introduction / 145 5.1 Coding Secrets / 145 Tossing a Coin into a Well The RSA Cryptosystem Digital Signatures 5.2 The Yao Millionaire Problem / 155 5.3 Check Digits .158 Basic Check Digit Schemes A Perfect Check Digit Method Beyond Perfection: Correcting Errors 5.4 Factoring Algorithms / 167 Trial Division Fermat's Algorithm Pollard Rho Pollard $p - 1$ The Current Scene Chapter 6. Quadratic Residues / 179 6.0 Introduction / 179 6.1 Pepin's Test / 119 Quadratic Residues Pepin's Test Primes Congruent to 1 (Mod 4) 6.2 Proof of Quadratic Reciprocity / 185 Gauss's Lemma Proof of Quadratic Reciprocity Jacobi's Extension An Application to Factoring 6.3 Quadratic Equations / 194 Chapter 7. Continued Fractions / 201 7.0 Introduction / 201 7.1 Finite Continued Fractions / 202 7.2 Infinite Continued Fractions / 207 7.3 Periodic Continued Fractions / 213 7.4 Pell's Equation / 227 7.5 Archimedes and the Sun God's Cattle / 232 Wurm's Version: Using Rectangular Bulls The Real Cattle Problem 7.6 Factoring via Continued Fractions / 238 Chapter 8. Prime Testing with Lucas Sequences / 247 8.0 Introduction / 247 8.1 Divisibility Properties of Lucas Sequences / 248 8.2 Prime Tests Using Lucas Sequences / 259 Lucas Certification The Lucas--Lehmer Algorithm Explained Lucas Pseudoprimes Strong Quadratic Pseudoprimes Primality Testing's Holy Grail Chapter 9. Prime Imaginaries and Imaginary Primes / 279 9.0 Introduction / 279 9.1 Sums of Two Squares / 279 Primes The General Problem How Many Ways Number Theory and Salt 9.2 The Gaussian Integers / 302 Complex Number Theory Gaussian Primes The Moat Problem The Gaussian Zoo 9.3 Higher Reciprocity / 325 Appendix A. Mathematica Basics / 333 A.0 Introduction / 333 A.1 Plotting / 336 A.2 Typesetting / 338 Sending Files By E-Mail A.3 Types of Functions / 341 A.4 Programs / 345 A.6 Solving Equations / 347 A.7 Symbolic Algebra / 349 Appendix B. Lucas Certificates Exist / 351 References / 355 Index of Mathematica Objects / 359 Subject Index / 363

shortTOC:
Fundamentals Congruences, equations, and powers Euler's function Prime numbers Some applications Quadratic residues Continued fractions Prime testing with Lucas sequences Prime imaginaries and imaginary primes Appendix A. Mathematica basics Appendix B. Lucas certificates exist

rawshortTOC:
Fundamentals \\ Congruences, equations, and powers \\ Euler's function \\ Prime numbers \\ Some applications \\ Quadratic residues \\ Continued fractions \\ Prime testing with Lucas sequences \\ Prime imaginaries and imaginary primes \\ Appendix A. Mathematica basics \\ Appendix B. Lucas certificates exist

rawTOC:
Preface Vv \\ Notation Xi \\ Chapter 1. Fundamentals / 1 \\ 1.0 Introduction / 1 \\ 1.1 A Famous Sequence of Numbers / 2 \\ 1.2 The Euclidean Algorithm / 6 \\ The Oldest Algorithm \\ Reversing the Euclidean Algorithm \\ The Extended GCD Algorithm \\ The Fundamental Theorem of Arithmetic \\ Two Applications \\ 1.3 Modular Arithmetic / 25 \\ 1.4 Fast Powers / 30 \\ A Fast Algorithm for Exponentiation \\ Powers of Matrices, Big-O Notation \\ Chapter 2. Congruences, Equations, and Powers / 41 \\ 2.0 Introduction / / 41 \\ 2.1 Solving Linear Congruences / 41 \\ Linear Diophantine Equations in Two Variables \\ Linear Equations in Several Variables \\ Linear Congruences \\ The Conductor \\ An Important Quadratic Congruence \\ 2.2 The Chinese Remainder Theorem / 49 \\ 2.3 PowerMod Patterns / 55 \\ Fermat's Little Theorem \\ More Patterns in Powers \\ 2.4 Pseudoprimes / 59 \\ Using the Pseudoprime Test \\ Chapter 3. Euler's $\phi$ Function / 65 \\ 3.0 Introduction / 65 \\ 3.1 Euler's $\phi$ Function / 656 \\ 3.2 Perfect Numbers and Their Relatives / 12 \\ The Sum of Divisors Function \\ Perfect Numbers \\ Amicable, Abundant, and Deficient Numbers \\ 3.3 Euler's Theorem / 81 \\ 3.4 Primitive Roots for Primes / 84 \\ The Order of an Integer \\ Primes Have Primitive Roots \\ Repeating Decimals \\ 3.5 Primitive Roots for Composites / 70 \\ 3.6 The Universal Exponent / 73 \\ Universal Exponents \\ Power Towers \\ The Form of Carmichael Numbers \\ Chapter 4. Prime Numbers / 99 \\ 4.0 Introduction / 99 \\ 4.1 The number of Primes / 100 \\ We'll Never Run Out of Primes \\ The Sieve of Eratosthenes \\ Chebyshev's Theorem and Bertrand's Postulate \\ 4.2 Prime Testing and Certification / 114 \\ Strong Pseudoprimes \\ Industrial-Grade Primes \\ Prime Certification Via Primitive Roots \\ An Improvement \\ Pratt Certificates \\ 4.3 Refinements and Other Directions / 131 \\ Other Primality Tests \\ Strong Liars Are Scarce \\ Finding the $n$th Prime \\ 4.4 A Dozen Prime Mysteries / 141 \\ 5.0 Introduction / 145 \\ 5.1 Coding Secrets / 145 \\ Tossing a Coin into a Well \\ The RSA Cryptosystem \\ Digital Signatures \\ 5.2 The Yao Millionaire Problem / 155 \\ 5.3 Check Digits .158 \\ Basic Check Digit Schemes \\ A Perfect Check Digit Method \\ Beyond Perfection: Correcting Errors \\ 5.4 Factoring Algorithms / 167 \\ Trial Division \\ Fermat's Algorithm \\ Pollard Rho \\ Pollard $p - 1$ \\ The Current Scene \\ Chapter 6. Quadratic Residues / 179 \\ 6.0 Introduction / 179 \\ 6.1 P{\'e}pin's Test / 119 \\ Quadratic Residues \\ P{\'e}pin's Test \\ Primes Congruent to 1 (Mod 4) \\ 6.2 Proof of Quadratic Reciprocity / 185 \\ Gauss's Lemma \\ Proof of Quadratic Reciprocity \\ Jacobi's Extension \\ An Application to Factoring \\ 6.3 Quadratic Equations / 194 \\ Chapter 7. Continued Fractions / 201 \\ 7.0 Introduction / 201 \\ 7.1 Finite Continued Fractions / 202 \\ 7.2 Infinite Continued Fractions / 207 \\ 7.3 Periodic Continued Fractions / 213 \\ 7.4 Pell's Equation / 227 \\ 7.5 Archimedes and the Sun God's Cattle / 232 \\ Wurm's Version: Using Rectangular Bulls \\ The Real Cattle Problem \\ 7.6 Factoring via Continued Fractions / 238 \\ Chapter 8. Prime Testing with Lucas Sequences / 247 \\ 8.0 Introduction / 247 \\ 8.1 Divisibility Properties of Lucas Sequences / 248 \\ 8.2 Prime Tests Using Lucas Sequences / 259 \\ Lucas Certification \\ The Lucas--Lehmer Algorithm Explained \\ Lucas Pseudoprimes \\ Strong Quadratic Pseudoprimes \\ Primality Testing's Holy Grail \\ Chapter 9. Prime Imaginaries and Imaginary Primes / 279 \\ 9.0 Introduction / 279 \\ 9.1 Sums of Two Squares / 279 \\ Primes \\ The General Problem \\ How Many Ways \\ Number Theory and Salt \\ 9.2 The Gaussian Integers / 302 \\ Complex Number Theory \\ Gaussian Primes \\ The Moat Problem \\ The Gaussian Zoo \\ 9.3 Higher Reciprocity / 325 \\ Appendix A. Mathematica Basics / 333 \\ A.0 Introduction / 333 \\ A.1 Plotting / 336 \\ A.2 Typesetting / 338 \\ Sending Files By E-Mail \\ A.3 Types of Functions / 341 \\ A.4 Programs / 345 \\ A.6 Solving Equations / 347 \\ A.7 Symbolic Algebra / 349 \\ Appendix B. Lucas Certificates Exist / 351 \\ References / 355 \\ Index of Mathematica Objects / 359 \\ Subject Index / 363

entry:
@Book{Bressoud:2000:CCN,
  author =       "David M. Bressoud and S. Wagon",
  title =        "A Course in Computational Number Theory",
  publisher =    "Key College Publishers in cooperation with Springer",
  address =      "New York, NY, USA",
  pages =        "xii + 367",
  year =         "2000",
  ISBN =         "1-930190-10-7",
  ISBN-13 =      "978-1-930190-10-8",
  LCCN =         "QA241 .B788 2000",
  bibdate =      "Fri Sep 26 14:29:31 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0818/99016037-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0818/99016037-t.html",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Fundamentals \\
                 Congruences, equations, and powers \\
                 Euler's function \\
                 Prime numbers \\
                 Some applications \\
                 Quadratic residues \\
                 Continued fractions \\
                 Prime testing with Lucas sequences \\
                 Prime imaginaries and imaginary primes \\
                 Appendix A. Mathematica basics \\
                 Appendix B. Lucas certificates exist",
  subject =      "Number theory; Algorithms",
  tableofcontents = "Preface Vv \\
                 Notation Xi \\
                 Chapter 1. Fundamentals / 1 \\
                 1.0 Introduction / 1 \\
                 1.1 A Famous Sequence of Numbers / 2 \\
                 1.2 The Euclidean Algorithm / 6 \\
                 The Oldest Algorithm \\
                 Reversing the Euclidean Algorithm \\
                 The Extended GCD Algorithm \\
                 The Fundamental Theorem of Arithmetic \\
                 Two Applications \\
                 1.3 Modular Arithmetic / 25 \\
                 1.4 Fast Powers / 30 \\
                 A Fast Algorithm for Exponentiation \\
                 Powers of Matrices, Big-O Notation \\
                 Chapter 2. Congruences, Equations, and Powers / 41 \\
                 2.0 Introduction / / 41 \\
                 2.1 Solving Linear Congruences / 41 \\
                 Linear Diophantine Equations in Two Variables \\
                 Linear Equations in Several Variables \\
                 Linear Congruences \\
                 The Conductor \\
                 An Important Quadratic Congruence \\
                 2.2 The Chinese Remainder Theorem / 49 \\
                 2.3 PowerMod Patterns / 55 \\
                 Fermat's Little Theorem \\
                 More Patterns in Powers \\
                 2.4 Pseudoprimes / 59 \\
                 Using the Pseudoprime Test \\
                 Chapter 3. Euler's $\phi$ Function / 65 \\
                 3.0 Introduction / 65 \\
                 3.1 Euler's $\phi$ Function / 656 \\
                 3.2 Perfect Numbers and Their Relatives / 12 \\
                 The Sum of Divisors Function \\
                 Perfect Numbers \\
                 Amicable, Abundant, and Deficient Numbers \\
                 3.3 Euler's Theorem / 81 \\
                 3.4 Primitive Roots for Primes / 84 \\
                 The Order of an Integer \\
                 Primes Have Primitive Roots \\
                 Repeating Decimals \\
                 3.5 Primitive Roots for Composites / 70 \\
                 3.6 The Universal Exponent / 73 \\
                 Universal Exponents \\
                 Power Towers \\
                 The Form of Carmichael Numbers \\
                 Chapter 4. Prime Numbers / 99 \\
                 4.0 Introduction / 99 \\
                 4.1 The number of Primes / 100 \\
                 We'll Never Run Out of Primes \\
                 The Sieve of Eratosthenes \\
                 Chebyshev's Theorem and Bertrand's Postulate \\
                 4.2 Prime Testing and Certification / 114 \\
                 Strong Pseudoprimes \\
                 Industrial-Grade Primes \\
                 Prime Certification Via Primitive Roots \\
                 An Improvement \\
                 Pratt Certificates \\
                 4.3 Refinements and Other Directions / 131 \\
                 Other Primality Tests \\
                 Strong Liars Are Scarce \\
                 Finding the $n$th Prime \\
                 4.4 A Dozen Prime Mysteries / 141 \\
                 5.0 Introduction / 145 \\
                 5.1 Coding Secrets / 145 \\
                 Tossing a Coin into a Well \\
                 The RSA Cryptosystem \\
                 Digital Signatures \\
                 5.2 The Yao Millionaire Problem / 155 \\
                 5.3 Check Digits .158 \\
                 Basic Check Digit Schemes \\
                 A Perfect Check Digit Method \\
                 Beyond Perfection: Correcting Errors \\
                 5.4 Factoring Algorithms / 167 \\
                 Trial Division \\
                 Fermat's Algorithm \\
                 Pollard Rho \\
                 Pollard $p - 1$ \\
                 The Current Scene \\
                 Chapter 6. Quadratic Residues / 179 \\
                 6.0 Introduction / 179 \\
                 6.1 P{\'e}pin's Test / 119 \\
                 Quadratic Residues \\
                 P{\'e}pin's Test \\
                 Primes Congruent to 1 (Mod 4) \\
                 6.2 Proof of Quadratic Reciprocity / 185 \\
                 Gauss's Lemma \\
                 Proof of Quadratic Reciprocity \\
                 Jacobi's Extension \\
                 An Application to Factoring \\
                 6.3 Quadratic Equations / 194 \\
                 Chapter 7. Continued Fractions / 201 \\
                 7.0 Introduction / 201 \\
                 7.1 Finite Continued Fractions / 202 \\
                 7.2 Infinite Continued Fractions / 207 \\
                 7.3 Periodic Continued Fractions / 213 \\
                 7.4 Pell's Equation / 227 \\
                 7.5 Archimedes and the Sun God's Cattle / 232 \\
                 Wurm's Version: Using Rectangular Bulls \\
                 The Real Cattle Problem \\
                 7.6 Factoring via Continued Fractions / 238 \\
                 Chapter 8. Prime Testing with Lucas Sequences / 247 \\
                 8.0 Introduction / 247 \\
                 8.1 Divisibility Properties of Lucas Sequences / 248
                 \\
                 8.2 Prime Tests Using Lucas Sequences / 259 \\
                 Lucas Certification \\
                 The Lucas--Lehmer Algorithm Explained \\
                 Lucas Pseudoprimes \\
                 Strong Quadratic Pseudoprimes \\
                 Primality Testing's Holy Grail \\
                 Chapter 9. Prime Imaginaries and Imaginary Primes / 279
                 \\
                 9.0 Introduction / 279 \\
                 9.1 Sums of Two Squares / 279 \\
                 Primes \\
                 The General Problem \\
                 How Many Ways \\
                 Number Theory and Salt \\
                 9.2 The Gaussian Integers / 302 \\
                 Complex Number Theory \\
                 Gaussian Primes \\
                 The Moat Problem \\
                 The Gaussian Zoo \\
                 9.3 Higher Reciprocity / 325 \\
                 Appendix A. Mathematica Basics / 333 \\
                 A.0 Introduction / 333 \\
                 A.1 Plotting / 336 \\
                 A.2 Typesetting / 338 \\
                 Sending Files By E-Mail \\
                 A.3 Types of Functions / 341 \\
                 A.4 Programs / 345 \\
                 A.6 Solving Equations / 347 \\
                 A.7 Symbolic Algebra / 349 \\
                 Appendix B. Lucas Certificates Exist / 351 \\
                 References / 355 \\
                 Index of Mathematica Objects / 359 \\
                 Subject Index / 363",
}


bibtype: article
filename: elefunt.bib
label: Brezinski:2000:CAD
author: C. Brezinski
title: Convergence acceleration during the 20th century
journal: j-J-COMPUT-APPL-MATH
volume: 122
number: 1--2
pages: 1--21
month: oct
monthnumber: 10
year: 2000
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(00)00360-5
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 65-03 (01A60)
MRnumber: 1794649
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
note: Numerical analysis 2000, Vol. II: Interpolation and extrapolation
fjournal: Journal of Computational and Applied Mathematics
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: C. Brezinski
rawnote: Numerical analysis 2000, Vol. II: Interpolation and extrapolation
rawtitle: Convergence acceleration during the 20th century
entry:
@Article{Brezinski:2000:CAD,
  author =       "C. Brezinski",
  title =        "Convergence acceleration during the 20th century",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "122",
  number =       "1--2",
  pages =        "1--21",
  month =        oct,
  year =         "2000",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00360-5",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65-03 (01A60)",
  MRnumber =     "1794649",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Numerical analysis 2000, Vol. II: Interpolation and
                 extrapolation",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Carlson:2000:RTE
author: B. C. Carlson and James FitzSimons
title: Reduction theorems for elliptic integrands with the square root of two quadratic factors
journal: j-J-COMPUT-APPL-MATH
volume: 118
number: 1--2
pages: 71--85
day: 1
month: jun
monthnumber: 6
year: 2000
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:43:35 MST 2017
bibtimestamp: 2017.02.25 12:43:35 MST
URL: http://www.sciencedirect.com/science/article/pii/S037704270000282X
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: B. C. Carlson and James FitzSimons
rawtitle: Reduction theorems for elliptic integrands with the square root of two quadratic factors
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib

entry:
@Article{Carlson:2000:RTE,
  author =       "B. C. Carlson and James FitzSimons",
  title =        "Reduction theorems for elliptic integrands with the
                 square root of two quadratic factors",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "118",
  number =       "1--2",
  pages =        "71--85",
  day =          "1",
  month =        jun,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:43:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270000282X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Cawley:2000:FCA
author: G. C. Cawley
title: On a Fast, Compact Approximation of the Exponential Function
journal: j-NEURAL-COMP
volume: 12
number: 9
pages: 2009--2012
day: 1
month: sep
monthnumber: 9
year: 2000
CODEN: NEUCEB
ISSN: 0899-7667 (print), 1530-888x (electronic) OR 08997667 (print), 1530888x (electronic)
ISSNL: 0899-7667 OR 08997667
bibdate: Fri Nov 8 05:39:32 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; Ingenta database
bibtimestamp: 2002.11.08 05:39:32 MST
fjournal: Neural Computation
acknowledgement: ack-nhfb
journalURL: http://www.mitpressjournals.org/loi/neco
rawauthor: G. C. Cawley
rawtitle: On a Fast, Compact Approximation of the Exponential Function
entry:
@Article{Cawley:2000:FCA,
  author =       "G. C. Cawley",
  title =        "On a Fast, Compact Approximation of the Exponential
                 Function",
  journal =      j-NEURAL-COMP,
  volume =       "12",
  number =       "9",
  pages =        "2009--2012",
  day =          "1",
  month =        sep,
  year =         "2000",
  CODEN =        "NEUCEB",
  ISSN =         "0899-7667 (print), 1530-888x (electronic)",
  ISSN-L =       "0899-7667",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Neural Computation",
  journal-URL =  "http://www.mitpressjournals.org/loi/neco",
  pagecount =    "4",
}


bibtype: article
filename: elefunt.bib
label: Cherri:2000:PCC
author: A. K. Cherri and M. S. Alam
title: Parallel computation of complex elementary functions using quaternary signed-digit arithmetic
journal: Optics and Laser Technology
volume: 32
number: 6
pages: 391--399
year: 2000
ISSN: 0030-3992 OR 00303992
bibdate: Sat Dec 7 09:21:28 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; Ingenta database
bibtimestamp: 2002.12.07 09:21:28 MST
acknowledgement: ack-nhfb
rawauthor: A. K. Cherri and M. S. Alam
rawtitle: Parallel computation of complex elementary functions using quaternary signed-digit arithmetic
entry:
@Article{Cherri:2000:PCC,
  author =       "A. K. Cherri and M. S. Alam",
  title =        "Parallel computation of complex elementary functions
                 using quaternary signed-digit arithmetic",
  journal =      "Optics and Laser Technology",
  volume =       "32",
  number =       "6",
  pages =        "391--399",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "0030-3992",
  bibdate =      "Sat Dec 7 09:21:28 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  pagecount =    "9",
}


bibtype: inproceedings
filename: elefunt.bib
label: Chu:2000:CPT
author: Wanming Chu and Yamin Li
booktitle: ACAC 2000: 5th Australasian Computer Architecture Conference
title: Cost / performance tradeoff of $n$-select square root implementations
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 9--16
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Wanming Chu and Yamin Li
rawbooktitle: {ACAC 2000}: 5th Australasian Computer Architecture Conference
rawtitle: Cost\slash performance tradeoff of $n$-select square root implementations
entry:
@InProceedings{Chu:2000:CPT,
  author =       "Wanming Chu and Yamin Li",
  booktitle =    "{ACAC 2000}: 5th Australasian Computer Architecture
                 Conference",
  title =        "Cost\slash performance tradeoff of $n$-select square
                 root implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "9--16",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Hardware square-root units require large numbers of
                 gates even for iterative implementations. In this paper
                 we present four low-cost high-performance
                 fully-pipelined n-select implementations (nS-Root)
                 based on a non-restoring-remainder square root
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Cohen:2000:CAA
author: Henri Cohen and Fernando Rodriguez Villegas and Don Zagier
title: Convergence Acceleration of Alternating Series
journal: j-EXP-MATH
volume: 9
number: 1
pages: 3--12
year: 2000
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 11Y55 (65B05)
MRnumber: 1758796 (2001m:11222)
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
URL: http://projecteuclid.org/euclid.em/1046889587; http://www.math.u-bordeaux.fr/~cohen/sumalt2new.ps
fjournal: Experimental Mathematics
keywords: convergence acceleration
ZMnumber: 0972.11115
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/uexm20
rawauthor: Henri Cohen and Fernando {Rodriguez Villegas} and Don Zagier
rawtitle: Convergence Acceleration of Alternating Series
abstract:
We discuss some linear acceleration methods for alternating series which are in theory and in practice much better than that of Euler--Van Wijngaarden. One of the algorithms, for instance, allows one to calculate $ sum ( - 1)^k a_k $ with an error of about $ 17.93^-n $ from the first $n$ terms for a wide class of sequences $ a_k $. Such methods are useful for high precision calculations frequently appearing in number theory.

rawabstract:
We discuss some linear acceleration methods for alternating series which are in theory and in practice much better than that of Euler--Van Wijngaarden. One of the algorithms, for instance, allows one to calculate $ \sum ( - 1)^k a_k $ with an error of about $ 17.93^{-n} $ from the first $n$ terms for a wide class of sequences $ \{ a_k \} $. Such methods are useful for high precision calculations frequently appearing in number theory.

entry:
@Article{Cohen:2000:CAA,
  author =       "Henri Cohen and Fernando {Rodriguez Villegas} and Don
                 Zagier",
  title =        "Convergence Acceleration of Alternating Series",
  journal =      j-EXP-MATH,
  volume =       "9",
  number =       "1",
  pages =        "3--12",
  year =         "2000",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11Y55 (65B05)",
  MRnumber =     "1758796 (2001m:11222)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://projecteuclid.org/euclid.em/1046889587;
                 http://www.math.u-bordeaux.fr/~cohen/sumalt2new.ps",
  ZMnumber =     "0972.11115",
  abstract =     "We discuss some linear acceleration methods for
                 alternating series which are in theory and in practice
                 much better than that of Euler--Van Wijngaarden. One of
                 the algorithms, for instance, allows one to calculate $
                 \sum ( - 1)^k a_k $ with an error of about $ 17.93^{-n}
                 $ from the first $n$ terms for a wide class of
                 sequences $ \{ a_k \} $. Such methods are useful for
                 high precision calculations frequently appearing in
                 number theory.",
  acknowledgement = ack-nhfb,
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Corless:2000:AAS
author: Robert M. Corless and James H. Davenport and David J. Jeffrey and Stephen M. Watt
title: ``According to Abramowitz and Stegun'' or $ arccoth $ needn't be uncouth
journal: j-SIGSAM
volume: 34
number: 2
pages: 58--65
month: jun
monthnumber: 6
year: 2000
CODEN: SIGSBZ
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Fri Feb 8 18:27:07 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/sigsam.bib
bibtimestamp: 2002.02.08 18:27:07 MST
fjournal: SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)
acknowledgement: ack-nhfb
ajournal: SIGSAM Bull.
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
issue: 132
rawauthor: Robert M. Corless and James H. Davenport and David J. Jeffrey and Stephen M. Watt
rawtitle: ``According to {Abramowitz and Stegun}'' or $ \arccoth $ needn't be uncouth
entry:
@Article{Corless:2000:AAS,
  author =       "Robert M. Corless and James H. Davenport and David J.
                 Jeffrey and Stephen M. Watt",
  title =        "``According to {Abramowitz and Stegun}'' or $ \arccoth
                 $ needn't be uncouth",
  journal =      j-SIGSAM,
  volume =       "34",
  number =       "2",
  pages =        "58--65",
  month =        jun,
  year =         "2000",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Fri Feb 8 18:27:07 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "SIGSAM Bull.",
  fjournal =     "SIGSAM Bulletin (ACM Special Interest Group on
                 Symbolic and Algebraic Manipulation)",
  issue =        "132",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}


bibtype: article
filename: elefunt.bib
label: Ercegovac:2000:IGD
author: Milos D. Ercegovac and Laurent Imbert and David W. Matula and Jean-Michel Muller and Guoheng Wei
title: Improving Goldschmidt Division, Square Root, and Square Root Reciprocal
journal: j-IEEE-TRANS-COMPUT
volume: 49
number: 7
pages: 759--763
month: jul
monthnumber: 7
year: 2000
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.863046
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Computers
remark: Selected papers from ARITH'14 cite Koren:1999:ISC.
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Milos D. Ercegovac and Laurent Imbert and David W. Matula and Jean-Michel Muller and Guoheng Wei
rawtitle: Improving {Goldschmidt} Division, Square Root, and Square Root Reciprocal
entry:
@Article{Ercegovac:2000:IGD,
  author =       "Milos D. Ercegovac and Laurent Imbert and David W.
                 Matula and Jean-Michel Muller and Guoheng Wei",
  title =        "Improving {Goldschmidt} Division, Square Root, and
                 Square Root Reciprocal",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "759--763",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863046",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  summary =      "The aim of this paper is to accelerate division,
                 square root, and square root reciprocal computations
                 when the Goldschmidt method is used on a pipelined
                 multiplier. This is done by replacing the last
                 iteration by the addition of a correcting term
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Ercegovac:2000:RSR
author: Milos D. Ercegovac and Tomas Lang and Jean-Michel Muller and Arnaud Tisserand
journal: j-IEEE-TRANS-COMPUT
volume: 49
number: 7
pages: 628--637
month: jul
monthnumber: 7
year: 2000
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.863031
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 68M07 (65B15)
MRnumber: MR1783602 (2001e:68016)
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Institute of Electrical and Electronics Engineers. Transactions on Computers
remark: Selected papers from ARITH'14 cite Koren:1999:ISC.
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Milos D. Ercegovac and Tom{\'a}s Lang and Jean-Michel Muller and Arnaud Tisserand
title:
Reciprocation, Square Root, Inverse Square Root, and Some Elementary Functions Using Small Multipliers

rawtitle:
Reciprocation, Square Root, Inverse Square Root, and Some Elementary Functions Using Small Multipliers

entry:
@Article{Ercegovac:2000:RSR,
  author =       "Milos D. Ercegovac and Tom{\'a}s Lang and Jean-Michel
                 Muller and Arnaud Tisserand",
  title =        "Reciprocation, Square Root, Inverse Square Root, and
                 Some Elementary Functions Using Small Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "628--637",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863031",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68M07 (65B15)",
  MRnumber =     "MR1783602 (2001e:68016)",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Institute of Electrical and Electronics Engineers.
                 Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  summary =      "This paper deals with the computation of reciprocals,
                 square roots, inverse square roots, and some elementary
                 functions using small tables, small multipliers, and,
                 for some functions, a final ``large'' (almost
                 full-length) multiplication. \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Favati:2000:SAC
author: P. Favati and G. Lotti and O. Menchi and F. Romani
title: Separable asymptotic cost of evaluating elementary functions
journal: j-NUMER-ALGORITHMS
volume: 24
number: 3
pages: 255--274
year: 2000
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 65Y20
MRnumber: MR1780414 (2001d:65174)
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; Ingenta database
bibtimestamp: 2005.04.13 06:46:35 ???
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: P. Favati and G. Lotti and O. Menchi and F. Romani
rawtitle: Separable asymptotic cost of evaluating elementary functions
entry:
@Article{Favati:2000:SAC,
  author =       "P. Favati and G. Lotti and O. Menchi and F. Romani",
  title =        "Separable asymptotic cost of evaluating elementary
                 functions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "24",
  number =       "3",
  pages =        "255--274",
  year =         "2000",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65Y20",
  MRnumber =     "MR1780414 (2001d:65174)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  pagecount =    "20",
}


bibtype: article
filename: elefunt.bib
label: Galue:2000:MTG
author: L. Galue and H. G. Khajah and Shyam L. Kalla
title: Multiplication theorems for generalized and double-index Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 118
number: 1--2
pages: 143--150
day: 1
month: jun
monthnumber: 6
year: 2000
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:43:35 MST 2017
bibtimestamp: 2017.02.25 12:43:35 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700002855
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: L. Galu{\'e} and H. G. Khajah and Shyam L. Kalla
rawtitle: Multiplication theorems for generalized and double-index {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib

entry:
@Article{Galue:2000:MTG,
  author =       "L. Galu{\'e} and H. G. Khajah and Shyam L. Kalla",
  title =        "Multiplication theorems for generalized and
                 double-index {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "118",
  number =       "1--2",
  pages =        "143--150",
  day =          "1",
  month =        jun,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:43:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700002855",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Harris:2000:SBE
author: Frank E. Harris
title: Spherical Bessel expansions of sine, cosine, and exponential integrals
journal: j-APPL-NUM-MATH
volume: 34
number: 1
pages: 95--98
month: jun
monthnumber: 6
year: 2000
CODEN: ANMAEL
DOI: https://doi.org/10.1016/S0168-9274(99)00031-8
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 33B10; 65D30 (33F05 65D20)
MRnumber: 1755696 (2001a:65027)
bibdate: Sat Oct 21 13:09:35 MDT 2000
bibtimestamp: 2000.10.21 13:09:35 MDT
fjournal: Applied Numerical Mathematics: Transactions of IMACS
ZMnumber: Zbl 0951.33002
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: Frank E. Harris
rawtitle: Spherical {Bessel} expansions of sine, cosine, and exponential integrals
bibsource:
http://www.elsevier.com/locate/issn/01689274; https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib; https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www.elsevier.nl/gej-ng/29/17/21/62/27/32/abstract.html; http://www.elsevier.nl/gej-ng/29/17/21/62/27/32/article.pdf; http://www.sciencedirect.com/science/article/pii/S0168927499000318

entry:
@Article{Harris:2000:SBE,
  author =       "Frank E. Harris",
  title =        "Spherical {Bessel} expansions of sine, cosine, and
                 exponential integrals",
  journal =      j-APPL-NUM-MATH,
  volume =       "34",
  number =       "1",
  pages =        "95--98",
  month =        jun,
  year =         "2000",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/S0168-9274(99)00031-8",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "33B10; 65D30 (33F05 65D20)",
  MRnumber =     "1755696 (2001a:65027)",
  bibdate =      "Sat Oct 21 13:09:35 MDT 2000",
  bibsource =    "http://www.elsevier.com/locate/issn/01689274;
                 https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.nl/gej-ng/29/17/21/62/27/32/abstract.html;
                 http://www.elsevier.nl/gej-ng/29/17/21/62/27/32/article.pdf;
                 http://www.sciencedirect.com/science/article/pii/S0168927499000318",
  ZMnumber =     "Zbl 0951.33002",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
}


bibtype: inproceedings
filename: elefunt.bib
label: Hasan:2000:FPI
author: M. A. Hasan and A. A. Hasan and S. Rahman
booktitle: Proceedings of the 39th IEEE Conference on Decision and Control
title: Fixed point iterations for computing square roots and the matrix sign function of complex matrices
volume: 5
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 4253--4258
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: M. A. Hasan and A. A. Hasan and S. Rahman
rawbooktitle: Proceedings of the 39th {IEEE} Conference on Decision and Control
rawtitle: Fixed point iterations for computing square roots and the matrix sign function of complex matrices
entry:
@InProceedings{Hasan:2000:FPI,
  author =       "M. A. Hasan and A. A. Hasan and S. Rahman",
  booktitle =    "Proceedings of the 39th {IEEE} Conference on Decision
                 and Control",
  title =        "Fixed point iterations for computing square roots and
                 the matrix sign function of complex matrices",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "4253--4258",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The purpose of this work has been the development of
                 new set of rational iterations for computing square
                 roots and the matrix sign function of complex matrices.
                 Given any positive integer r{\&}ges;2, we presented a
                 systematic way of deriving rth order \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Hassibi:2000:ESR
author: B. Hassibi
title: An efficient square-root algorithm for BLAST
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: II737--II740
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: B. Hassibi
rawtitle: An efficient square-root algorithm for {BLAST}
booktitle:
Proceedings. 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing: ICASSP '00, 5--9 June 2000

rawbooktitle:
Proceedings. 2000 {IEEE} International Conference on Acoustics, Speech, and Signal Processing: {ICASSP '00}, 5--9 June 2000

entry:
@InProceedings{Hassibi:2000:ESR,
  author =       "B. Hassibi",
  booktitle =    "Proceedings. 2000 {IEEE} International Conference on
                 Acoustics, Speech, and Signal Processing: {ICASSP '00},
                 5--9 June 2000",
  title =        "An efficient square-root algorithm for {BLAST}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II737--II740",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Bell Labs Layered Space-Time (BLAST) is a scheme for
                 transmitting information over a rich-scattering
                 wireless environment using multiple receive and
                 transmit antennas. The main computational bottleneck in
                 the BLAST algorithm is a ``nulling and \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Hassibi:2000:FSR
author: B. Hassibi
booktitle: Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, 2000
title: A fast square-root implementation for BLAST
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1255--1259
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: B. Hassibi
rawtitle: A fast square-root implementation for {BLAST}
rawbooktitle:
{Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, 2000}

entry:
@InProceedings{Hassibi:2000:FSR,
  author =       "B. Hassibi",
  booktitle =    "{Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000}",
  title =        "A fast square-root implementation for {BLAST}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1255--1259",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Bell Labs Layered Space-Time (BLAST) is a scheme for
                 transmitting information over a rich-scattering
                 wireless environment using multiple receive and
                 transmit antennas. The main computational bottleneck in
                 the BLAST algorithm is a ``nulling and \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Holmgren:2000:CAL
author: Sverker Holmgren and Henrik Branden and Erik Sterner
journal: j-SIAM-J-SCI-COMP
volume: 21
number: 4
pages: 1524--1550
month: jul
monthnumber: 7
year: 2000
CODEN: SJOCE3
DOI: https://doi.org/10.1137/S1064827597317983
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
bibdate: Fri Oct 27 13:32:22 MDT 2000
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SISC/21/4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2000.10.27 13:32:22 MDT
URL: http://epubs.siam.org/sam-bin/dbq/article/31798
fjournal: SIAM Journal on Scientific Computing
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sisc
rawauthor: Sverker Holmgren and Henrik Brand{\'e}n and Erik Sterner
title:
Convergence Acceleration for the Linearized Navier--Stokes Equations using Semicirculant Approximations

rawtitle:
Convergence Acceleration for the Linearized {Navier--Stokes} Equations using Semicirculant Approximations

entry:
@Article{Holmgren:2000:CAL,
  author =       "Sverker Holmgren and Henrik Brand{\'e}n and Erik
                 Sterner",
  title =        "Convergence Acceleration for the Linearized
                 {Navier--Stokes} Equations using Semicirculant
                 Approximations",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "21",
  number =       "4",
  pages =        "1524--1550",
  month =        jul,
  year =         "2000",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827597317983",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Oct 27 13:32:22 MDT 2000",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/21/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/31798",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "convergence acceleration",
}


bibtype: misc
filename: elefunt.bib
label: Intel:2000:DSR
author: Intel
title: Divide, Square Root, and Remainder Algorithms for the Itanium Architecture
pages: 1524--1550
month: jul
monthnumber: 7
year: 2000
bibdate: Fri Sep 22 17:06:23 2023
bibtimestamp: 2023.09.22 17:06:23 ???
URL: https://studylib.net/doc/7921762/divide--square-root-and-remainder-algorithms-for-the-ia-64
acknowledgement: ack-nhfb
howpublished: Intel Software Development Products
rawauthor: {Intel}
rawtitle: Divide, Square Root, and Remainder Algorithms for the {Itanium} Architecture
entry:
@Misc{Intel:2000:DSR,
  author =       "{Intel}",
  title =        "Divide, Square Root, and Remainder Algorithms for the
                 {Itanium} Architecture",
  howpublished = "Intel Software Development Products",
  month =        jul,
  year =         "2000",
  bibdate =      "Fri Sep 22 17:06:23 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://studylib.net/doc/7921762/divide--square-root-and-remainder-algorithms-for-the-ia-64",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Jeffrey:2000:HMF
author: Alan Jeffrey
title: Handbook of Mathematical Formulas and Integrals
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
edition: Second
pages: xxvi + 433
year: 2000
ISBN: 0-12-382251-3 OR 0123822513
ISBN13: 978-0-12-382251-2 OR 9780123822512
LCCN: QA47 .J38 2000
bibdate: Wed Jun 12 14:47:49 MDT 2024
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.06.12 14:47:49 MDT
subject: Mathematics; Tables; Formulae; Mathematics.
acknowledgement: ack-nhfb
rawauthor: Alan Jeffrey
rawtitle: Handbook of Mathematical Formulas and Integrals
TOC:
0: Quick Reference List of Frequently Used Data 0.1: Useful Identities / 1 0.2: Complex Relationships / 2 0.3: Constants / 2 0.4: Derivatives of Elementary Functions / 3 0.5: Rules of Differentiation and Integration / 3 0.6: Standard Integrals / 4 0.7: Standard Series / 11 0.8: Geometry / 13 1: Numerical, Algebraic, and Analytical Results for Series and Calculus 1.1: Algebraic Results Involving Real and Complex Numbers / 25 1.2: Finite Sums / 29 1.3: Bernoulli and Euler Numbers and Polynomials / 37 1.4: Determinants / 47 1.5: Matrices / 55 1.6: Permutations and Combinations / 62 1.7: Partial Fraction Decomposition / 63 1.8: Convergence of Series / 66 1.9: Infinite Products / 71 1.10: Functional Series / 73 1.11: Power Series / 74 1.12: Taylor Series / 79 4.13: Fourier Series / 81 4.14: Asymptotic Expansions / 85 1.15: Basic Results from the Calculus / 86 2: Functions and Identities 2.1: Complex Numbers and Trigonometric and Hyperbolic Functions / 101 2.2: Logarithms and Exponentials / 112 2.3: Exponential Function / 114 2.4: Trigonometric Identities / 115 2.5: Hyperbolic Identities / 121 2.6: Logarithm / 126 2.7: Inverse Trigonometric and Hyperbolic Functions 128 2.8: Series Representations of Trigonometric and Hyperbolic Functions / 133 2.9: Useful Limiting Values and Inequalities Involving Elementary Functions / 136 3: Derivatives of Elementary Functions 3.1: Derivatives of Algebraic, Logarithmic, and Exponential Functions / 139 3.2: Derivatives of Trigonometric Functions / 140 3.3: Derivatives of Inverse Trigonometric Functions 140 3.4: Derivatives of Hyperbolic Functions / 141 3.5: Derivatives of Inverse Hyperbolic Functions 142 4: Indefinite Integrals of Algebraic Functions 4.1: Algebraic and Transcendental Functions / 145 4.2: Indefinite Integrals of Rational Functions / 146 4.3: Nonrational Algebraic Functions / 158 5: Indefinite Integrals of Exponential Functions 5.1: Basic Results / 167 6: Indefinite Integrals of Logarithmic Functions 6.1: Combinations of Logarithms and Polynomials / 173 7: Indefinite Integrals of Hyperbolic Functions 7.1: Basic Results / 179 7.2: Integrands Involving Powers of sinh(bx) or cosh(bx) / 180 7.3: Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) / 181 7.4: Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x / 183 7.5: Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x / 183 7.6: Integrands Involving (1 [plus or minus] cosh x)[superscript -m] / 185 7.7: Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x / 185 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d) / 186 7.9: Integrands Involving tanh kx and coth kx / 188 7.10: Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx / 189 8: Indefinite Integrals Involving Inverse Hyperbolic Functions 8.1: Basic Results / 191 8.2: Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) / 193 8.3: Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) / 194 8.4: Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195 9: Indefinite Integrals of Trigonometric Functions 9.1: Basic Results / 197 9.2: Integrands Involving Powers of x and Powers of sin x or cos x / 197 9.3: Integrands Involving tan x and/or cot x / 205 9.4: Integrands Involving sin x and cos x / 207 9.5: Integrands Involving Sines and Cosines with Linear Arguments and Powers of x / 211 10: Indefinite Integrals of Inverse Trigonometric Functions 10.1: Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions 215 --. 11: Gamma, Beta, Pi, and Psi Functions 11.1: Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) / 221 12: Elliptic Integrals and Functions 12.1: Elliptic Integrals / 229 12.2: Jacobian Elliptic Functions / 235 12.3: Derivatives and Integrals / 237 12.4: Inverse Jacobian Elliptic Functions / 237 13: Probability Integrals and the Error Function 13.1: Normal Distribution / 239 13.2: Error Function / 242 14: Fresnel Integrals, Sine and Cosine Integrals 14.1: Definitions, Series Representations, and Values at Infinity / 245 14.2: Definitions, Series Representations, and Values at Infinity / 247 15: Definite Integrals 15.1: Integrands Involving Powers of x / 249 15.2: Integrands Involving Trigonometric Functions 251 15.3: Integrands Involving the Exponential Function 254 15.4: Integrands Involving the Hyperbolic Function 256 15.5: Integrands Involving the Logarithmic Function 256 16: Different Forms of Fourier Series 16.1: Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 257 16.2: Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L / 258 16.3: Fourier Series for f(x) on a [less than or equal] x [less than or equal] b / 258 16.4: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 259 16.5: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L / 259 16.6: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 260 16.7: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L / 260 16.8: Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 260 16.9: Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L 261 16.10: Representative Examples of Fourier Series 261 16.11: Fourier Series and Discontinuous Functions 265 17: Bessel Functions 17.1: Bessel's Differential Equation / 269 17.2: Series Expansions for J[subscript v](x) and Y[subscript v](x) / 270 17.3: Bessel Functions of Fractional Order / 272 17.4: Asymptotic Representations for Bessel Functions / 273 17.5: Zeros of Bessel Functions / 273 17.6: Bessel's Modified Equation / 274 17.7: Series Expansions for I[subscript v](x) and K[subscript v](x) / 276 17.8: Modified Bessel Functions of Fractional Order 277 17.9: Asymptotic Representations of Modified Bessel Functions / 278 17.10: Relationships between Bessel Functions / 278 17.11: Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) / 281 17.12: Indefinite Integrals of Bessel Functions / 281 17.13: Definite Integrals Involving Bessel Functions / 282 17.14: Spherical Bessel Functions / 283 18: Orthogonal Polynomials 18.2: Legendre Polynomials P[subscript n](x) / 286 18.3: Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) / 290 18.4: Laguerre Polynomials L[subscript n](x) / 294 18.5: Hermite Polynomials H[subscript n](x) / 296 19: Laplace Transformation 20: Fourier Transforms 21: Numerical Integration 21.1: Classical Methods / 315 22: Solutions of Standard Ordinary Differential Equations 22.2: Separation of Variables / 323 22.3: Linear First-Order Equations / 323 22.4: Bernoulli's Equation / 324 22.5: Exact Equations / 325 22.6: Homogeneous Equations / 325 22.7: Linear Differential Equations / 326 22.8: Constant Coefficient Linear Differential Equations--Homogeneous Case / 327 22.9: Linear Homogeneous Second-Order Equation / 330 22.10: Constant Coefficient Linear Differential Equations--Inhomogeneous Case / 331 22.11: Linear Inhomogeneous Second-Order Equation 333 22.12: Determination of Particular Integrals by the Method of- Undetermined Coefficients / 334 22.13: Cauchy-Euler Equation / 336 22.14: Legendre's Equation / 337 22.15: Bessel's Equations / 337 22.16: Power Series and Frobenius Methods / 339 22.17: Hypergeometric Equation / 344 22.18: Numerical Methods / 345 23: Vector Analysis 23.1: Scalars and Vectors / 353 23.2: Scalar Products / 358 23.3: Vector Products / 359 23.4: Triple Products / 360 23.5: Products of Four Vectors / 361 23.6: Derivatives of Vector Functions of a Scalar t 361 23.7: Derivatives of Vector Functions of Several Scalar Variables / 362 23.8: Integrals of Vector Functions of a Scalar Variable t / 363 23.9: Line Integrals / 364 23.10: Vector Integral Theorems / 366 23.11: A Vector Rate of Change Theorem / 368 23.12: Useful Vector Identities and Results / 368 24: Systems of Orthogonal Coordinates 24.1: Curvilinear Coordinates / 369 24.2: Vector Operators in Orthogonal Coordinates 371 24.3: Systems of Orthogonal Coordinates / 371 25: Partial Differential Equations and Special Functions 25.1: Fundamental Ideas / 381 25.2: Method of Separation of Variables / 385 25.3: Sturm--Liouville Problem and Special Functions 387 25.4: A First-Order System and the Wave Equation 390 25.5: Conservation Equations (Laws) / 391 25.6: Method of Characteristics / 392 25.7: Discontinuous Solutions (Shocks) / 396 25.8: Similarity Solutions / 398 25.9: Burgers's Equation, the KdV Equation, and the KdVB Equation / 400 26: Z-Transform 26.1: Z-Transform and Transform Pairs / 403 27: Numerical Approximation 27.2: Economization of Series / 411 27.3: Pade Approximation / 413 27.4: Finite Difference Approximations to Ordinary and Partial Derivatives / 415

shortTOC:
0: Quick Reference List of Frequently Used Data 1: Numerical, Algebraic, and Analytical Results for Series and Calculus 2: Functions and Identities 3: Derivatives of Elementary Functions 4: Indefinite Integrals of Algebraic Functions 5: Indefinite Integrals of Exponential Functions 6: Indefinite Integrals of Logarithmic Functions 7: Indefinite Integrals of Hyperbolic Functions 8: Indefinite Integrals Involving Inverse Hyperbolic Functions 9: Indefinite Integrals of Trigonometric Functions 10: Indefinite Integrals of Inverse Trigonometric Functions 11: The Gamma, Beta, Pi, and Psi Functions 12: Elliptic Integrals and Functions 13: Probability Integrals and the Error Function 14: Fresnel Integrals 15: Definite Integrals 16: Different Forms of Fourier Series 17: Bessel Functions 18: Orthogonal Polynomials 19: Laplace Transformation 20: Fourier Transforms 21: Numerical Integration 22: Solutions of Standard Ordinary Differential Equations 23: Vector Analysis 24: Systems of Orthogonal Coordinates 25: Partial Differential Equations and Special Functions

rawshortTOC:
0: Quick Reference List of Frequently Used Data \\ 1: Numerical, Algebraic, and Analytical Results for Series and Calculus \\ 2: Functions and Identities \\ 3: Derivatives of Elementary Functions \\ 4: Indefinite Integrals of Algebraic Functions \\ 5: Indefinite Integrals of Exponential Functions \\ 6: Indefinite Integrals of Logarithmic Functions \\ 7: Indefinite Integrals of Hyperbolic Functions \\ 8: Indefinite Integrals Involving Inverse Hyperbolic Functions \\ 9: Indefinite Integrals of Trigonometric Functions \\ 10: Indefinite Integrals of Inverse Trigonometric Functions \\ 11: The Gamma, Beta, Pi, and Psi Functions \\ 12: Elliptic Integrals and Functions \\ 13: Probability Integrals and the Error Function \\ 14: Fresnel Integrals \\ 15: Definite Integrals \\ 16: Different Forms of Fourier Series \\ 17: Bessel Functions \\ 18: Orthogonal Polynomials \\ 19: Laplace Transformation \\ 20: Fourier Transforms \\ 21: Numerical Integration \\ 22: Solutions of Standard Ordinary Differential Equations \\ 23: Vector Analysis \\ 24: Systems of Orthogonal Coordinates \\ 25: Partial Differential Equations and Special Functions

rawTOC:
0: Quick Reference List of Frequently Used Data \\ 0.1: Useful Identities / 1 \\ 0.2: Complex Relationships / 2 \\ 0.3: Constants / 2 \\ 0.4: Derivatives of Elementary Functions / 3 \\ 0.5: Rules of Differentiation and Integration / 3 \\ 0.6: Standard Integrals / 4 \\ 0.7: Standard Series / 11 \\ 0.8: Geometry / 13 \\ 1: Numerical, Algebraic, and Analytical Results for Series and Calculus \\ 1.1: Algebraic Results Involving Real and Complex Numbers / 25 \\ 1.2: Finite Sums / 29 \\ 1.3: Bernoulli and Euler Numbers and Polynomials / 37 \\ 1.4: Determinants / 47 \\ 1.5: Matrices / 55 \\ 1.6: Permutations and Combinations / 62 \\ 1.7: Partial Fraction Decomposition / 63 \\ 1.8: Convergence of Series / 66 \\ 1.9: Infinite Products / 71 \\ 1.10: Functional Series / 73 \\ 1.11: Power Series / 74 \\ 1.12: Taylor Series / 79 \\ 4.13: Fourier Series / 81 \\ 4.14: Asymptotic Expansions / 85 \\ 1.15: Basic Results from the Calculus / 86 \\ 2: Functions and Identities \\ 2.1: Complex Numbers and Trigonometric and Hyperbolic Functions / 101 \\ 2.2: Logarithms and Exponentials / 112 \\ 2.3: Exponential Function / 114 \\ 2.4: Trigonometric Identities / 115 \\ 2.5: Hyperbolic Identities / 121 \\ 2.6: Logarithm / 126 \\ 2.7: Inverse Trigonometric and Hyperbolic Functions 128 \\ 2.8: Series Representations of Trigonometric and Hyperbolic Functions / 133 \\ 2.9: Useful Limiting Values and Inequalities Involving Elementary Functions / 136 \\ 3: Derivatives of Elementary Functions \\ 3.1: Derivatives of Algebraic, Logarithmic, and Exponential Functions / 139 \\ 3.2: Derivatives of Trigonometric Functions / 140 \\ 3.3: Derivatives of Inverse Trigonometric Functions 140 \\ 3.4: Derivatives of Hyperbolic Functions / 141 \\ 3.5: Derivatives of Inverse Hyperbolic Functions 142 \\ 4: Indefinite Integrals of Algebraic Functions \\ 4.1: Algebraic and Transcendental Functions / 145 \\ 4.2: Indefinite Integrals of Rational Functions / 146 \\ 4.3: Nonrational Algebraic Functions / 158 \\ 5: Indefinite Integrals of Exponential Functions \\ 5.1: Basic Results / 167 \\ 6: Indefinite Integrals of Logarithmic Functions \\ 6.1: Combinations of Logarithms and Polynomials / 173 \\ 7: Indefinite Integrals of Hyperbolic Functions \\ 7.1: Basic Results / 179 \\ 7.2: Integrands Involving Powers of sinh(bx) or cosh(bx) / 180 \\ 7.3: Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) / 181 \\ 7.4: Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x / 183 \\ 7.5: Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x / 183 \\ 7.6: Integrands Involving (1 [plus or minus] cosh x)[superscript -m] / 185 \\ 7.7: Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x / 185 \\ 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d) / 186 \\ 7.9: Integrands Involving tanh kx and coth kx / 188 \\ 7.10: Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx / 189 \\ 8: Indefinite Integrals Involving Inverse Hyperbolic Functions \\ 8.1: Basic Results / 191 \\ 8.2: Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) / 193 \\ 8.3: Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) / 194 \\ 8.4: Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195 \\ 9: Indefinite Integrals of Trigonometric Functions \\ 9.1: Basic Results / 197 \\ 9.2: Integrands Involving Powers of x and Powers of sin x or cos x / 197 \\ 9.3: Integrands Involving tan x and/or cot x / 205 \\ 9.4: Integrands Involving sin x and cos x / 207 \\ 9.5: Integrands Involving Sines and Cosines with Linear Arguments and Powers of x / 211 \\ 10: Indefinite Integrals of Inverse Trigonometric Functions \\ 10.1: Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions 215 --. 11: Gamma, Beta, Pi, and Psi Functions \\ 11.1: Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) / 221 \\ 12: Elliptic Integrals and Functions \\ 12.1: Elliptic Integrals / 229 \\ 12.2: Jacobian Elliptic Functions / 235 \\ 12.3: Derivatives and Integrals / 237 \\ 12.4: Inverse Jacobian Elliptic Functions / 237 \\ 13: Probability Integrals and the Error Function \\ 13.1: Normal Distribution / 239 \\ 13.2: Error Function / 242 \\ 14: Fresnel Integrals, Sine and Cosine Integrals \\ 14.1: Definitions, Series Representations, and Values at Infinity / 245 \\ 14.2: Definitions, Series Representations, and Values at Infinity / 247 \\ 15: Definite Integrals \\ 15.1: Integrands Involving Powers of x / 249 \\ 15.2: Integrands Involving Trigonometric Functions 251 \\ 15.3: Integrands Involving the Exponential Function 254 \\ 15.4: Integrands Involving the Hyperbolic Function 256 \\ 15.5: Integrands Involving the Logarithmic Function 256 \\ 16: Different Forms of Fourier Series \\ 16.1: Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 257 \\ 16.2: Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L / 258 \\ 16.3: Fourier Series for f(x) on a [less than or equal] x [less than or equal] b / 258 \\ 16.4: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 259 \\ 16.5: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L / 259 \\ 16.6: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 260 \\ 16.7: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L / 260 \\ 16.8: Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 260 \\ 16.9: Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L 261 \\ 16.10: Representative Examples of Fourier Series 261 \\ 16.11: Fourier Series and Discontinuous Functions 265 \\ 17: Bessel Functions \\ 17.1: Bessel's Differential Equation / 269 \\ 17.2: Series Expansions for J[subscript v](x) and Y[subscript v](x) / 270 \\ 17.3: Bessel Functions of Fractional Order / 272 \\ 17.4: Asymptotic Representations for Bessel Functions / 273 \\ 17.5: Zeros of Bessel Functions / 273 \\ 17.6: Bessel's Modified Equation / 274 \\ 17.7: Series Expansions for I[subscript v](x) and K[subscript v](x) / 276 \\ 17.8: Modified Bessel Functions of Fractional Order 277 \\ 17.9: Asymptotic Representations of Modified Bessel Functions / 278 \\ 17.10: Relationships between Bessel Functions / 278 \\ 17.11: Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) / 281 \\ 17.12: Indefinite Integrals of Bessel Functions / 281 \\ 17.13: Definite Integrals Involving Bessel Functions / 282 \\ 17.14: Spherical Bessel Functions / 283 \\ 18: Orthogonal Polynomials \\ 18.2: Legendre Polynomials P[subscript n](x) / 286 \\ 18.3: Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) / 290 \\ 18.4: Laguerre Polynomials L[subscript n](x) / 294 \\ 18.5: Hermite Polynomials H[subscript n](x) / 296 \\ 19: Laplace Transformation \\ 20: Fourier Transforms \\ 21: Numerical Integration \\ 21.1: Classical Methods / 315 \\ 22: Solutions of Standard Ordinary Differential Equations \\ 22.2: Separation of Variables / 323 \\ 22.3: Linear First-Order Equations / 323 \\ 22.4: Bernoulli's Equation / 324 \\ 22.5: Exact Equations / 325 \\ 22.6: Homogeneous Equations / 325 \\ 22.7: Linear Differential Equations / 326 \\ 22.8: Constant Coefficient Linear Differential Equations--Homogeneous Case / 327 \\ 22.9: Linear Homogeneous Second-Order Equation / 330 \\ 22.10: Constant Coefficient Linear Differential Equations--Inhomogeneous Case / 331 \\ 22.11: Linear Inhomogeneous Second-Order Equation 333 \\ 22.12: Determination of Particular Integrals by the Method of- Undetermined Coefficients / 334 \\ 22.13: Cauchy-Euler Equation / 336 \\ 22.14: Legendre's Equation / 337 \\ 22.15: Bessel's Equations / 337 \\ 22.16: Power Series and Frobenius Methods / 339 \\ 22.17: Hypergeometric Equation / 344 \\ 22.18: Numerical Methods / 345 \\ 23: Vector Analysis \\ 23.1: Scalars and Vectors / 353 \\ 23.2: Scalar Products / 358 \\ 23.3: Vector Products / 359 \\ 23.4: Triple Products / 360 \\ 23.5: Products of Four Vectors / 361 \\ 23.6: Derivatives of Vector Functions of a Scalar t 361 \\ 23.7: Derivatives of Vector Functions of Several Scalar Variables / 362 \\ 23.8: Integrals of Vector Functions of a Scalar Variable t / 363 \\ 23.9: Line Integrals / 364 \\ 23.10: Vector Integral Theorems / 366 \\ 23.11: A Vector Rate of Change Theorem / 368 \\ 23.12: Useful Vector Identities and Results / 368 \\ 24: Systems of Orthogonal Coordinates \\ 24.1: Curvilinear Coordinates / 369 \\ 24.2: Vector Operators in Orthogonal Coordinates 371 \\ 24.3: Systems of Orthogonal Coordinates / 371 \\ 25: Partial Differential Equations and Special Functions \\ 25.1: Fundamental Ideas / 381 \\ 25.2: Method of Separation of Variables / 385 \\ 25.3: Sturm--Liouville Problem and Special Functions 387 \\ 25.4: A First-Order System and the Wave Equation 390 \\ 25.5: Conservation Equations (Laws) / 391 \\ 25.6: Method of Characteristics / 392 \\ 25.7: Discontinuous Solutions (Shocks) / 396 \\ 25.8: Similarity Solutions / 398 \\ 25.9: Burgers's Equation, the KdV Equation, and the KdVB Equation / 400 \\ 26: Z-Transform \\ 26.1: Z-Transform and Transform Pairs / 403 \\ 27: Numerical Approximation \\ 27.2: Economization of Series / 411 \\ 27.3: Pade Approximation / 413 \\ 27.4: Finite Difference Approximations to Ordinary and Partial Derivatives / 415

entry:
@Book{Jeffrey:2000:HMF,
  author =       "Alan Jeffrey",
  title =        "Handbook of Mathematical Formulas and Integrals",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  edition =      "Second",
  pages =        "xxvi + 433",
  year =         "2000",
  ISBN =         "0-12-382251-3",
  ISBN-13 =      "978-0-12-382251-2",
  LCCN =         "QA47 .J38 2000",
  bibdate =      "Wed Jun 12 14:47:49 MDT 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "0: Quick Reference List of Frequently Used
                 Data \\
                 1: Numerical, Algebraic, and Analytical Results for
                 Series and Calculus \\
                 2: Functions and Identities \\
                 3: Derivatives of Elementary Functions \\
                 4: Indefinite Integrals of Algebraic Functions \\
                 5: Indefinite Integrals of Exponential Functions \\
                 6: Indefinite Integrals of Logarithmic Functions \\
                 7: Indefinite Integrals of Hyperbolic Functions \\
                 8: Indefinite Integrals Involving Inverse Hyperbolic
                 Functions \\
                 9: Indefinite Integrals of Trigonometric Functions \\
                 10: Indefinite Integrals of Inverse Trigonometric
                 Functions \\
                 11: The Gamma, Beta, Pi, and Psi Functions \\
                 12: Elliptic Integrals and Functions \\
                 13: Probability Integrals and the Error Function \\
                 14: Fresnel Integrals \\
                 15: Definite Integrals \\
                 16: Different Forms of Fourier Series \\
                 17: Bessel Functions \\
                 18: Orthogonal Polynomials \\
                 19: Laplace Transformation \\
                 20: Fourier Transforms \\
                 21: Numerical Integration \\
                 22: Solutions of Standard Ordinary Differential
                 Equations \\
                 23: Vector Analysis \\
                 24: Systems of Orthogonal Coordinates \\
                 25: Partial Differential Equations and Special
                 Functions",
  subject =      "Mathematics; Tables; Formulae; Mathematics.",
  tableofcontents = "0: Quick Reference List of Frequently Used Data \\
                 0.1: Useful Identities / 1 \\
                 0.2: Complex Relationships / 2 \\
                 0.3: Constants / 2 \\
                 0.4: Derivatives of Elementary Functions / 3 \\
                 0.5: Rules of Differentiation and Integration / 3 \\
                 0.6: Standard Integrals / 4 \\
                 0.7: Standard Series / 11 \\
                 0.8: Geometry / 13 \\
                 1: Numerical, Algebraic, and Analytical Results for
                 Series and Calculus \\
                 1.1: Algebraic Results Involving Real and Complex
                 Numbers / 25 \\
                 1.2: Finite Sums / 29 \\
                 1.3: Bernoulli and Euler Numbers and Polynomials / 37
                 \\
                 1.4: Determinants / 47 \\
                 1.5: Matrices / 55 \\
                 1.6: Permutations and Combinations / 62 \\
                 1.7: Partial Fraction Decomposition / 63 \\
                 1.8: Convergence of Series / 66 \\
                 1.9: Infinite Products / 71 \\
                 1.10: Functional Series / 73 \\
                 1.11: Power Series / 74 \\
                 1.12: Taylor Series / 79 \\
                 4.13: Fourier Series / 81 \\
                 4.14: Asymptotic Expansions / 85 \\
                 1.15: Basic Results from the Calculus / 86 \\
                 2: Functions and Identities \\
                 2.1: Complex Numbers and Trigonometric and Hyperbolic
                 Functions / 101 \\
                 2.2: Logarithms and Exponentials / 112 \\
                 2.3: Exponential Function / 114 \\
                 2.4: Trigonometric Identities / 115 \\
                 2.5: Hyperbolic Identities / 121 \\
                 2.6: Logarithm / 126 \\
                 2.7: Inverse Trigonometric and Hyperbolic Functions 128
                 \\
                 2.8: Series Representations of Trigonometric and
                 Hyperbolic Functions / 133 \\
                 2.9: Useful Limiting Values and Inequalities Involving
                 Elementary Functions / 136 \\
                 3: Derivatives of Elementary Functions \\
                 3.1: Derivatives of Algebraic, Logarithmic, and
                 Exponential Functions / 139 \\
                 3.2: Derivatives of Trigonometric Functions / 140 \\
                 3.3: Derivatives of Inverse Trigonometric Functions 140
                 \\
                 3.4: Derivatives of Hyperbolic Functions / 141 \\
                 3.5: Derivatives of Inverse Hyperbolic Functions 142
                 \\
                 4: Indefinite Integrals of Algebraic Functions \\
                 4.1: Algebraic and Transcendental Functions / 145 \\
                 4.2: Indefinite Integrals of Rational Functions / 146
                 \\
                 4.3: Nonrational Algebraic Functions / 158 \\
                 5: Indefinite Integrals of Exponential Functions \\
                 5.1: Basic Results / 167 \\
                 6: Indefinite Integrals of Logarithmic Functions \\
                 6.1: Combinations of Logarithms and Polynomials / 173
                 \\
                 7: Indefinite Integrals of Hyperbolic Functions \\
                 7.1: Basic Results / 179 \\
                 7.2: Integrands Involving Powers of sinh(bx) or
                 cosh(bx) / 180 \\
                 7.3: Integrands Involving (a [plus or minus]
                 bx)[superscript m] sinh(cx) or (a + bx)[superscript m]
                 cosh(cx) / 181 \\
                 7.4: Integrands Involving x[superscript m]
                 sinh[superscript n] x or x[superscript m]
                 cosh[superscript n] x / 183 \\
                 7.5: Integrands Involving x[superscript m]
                 sinh[superscript -n] x or x[superscript m]
                 cosh[superscript -n] x / 183 \\
                 7.6: Integrands Involving (1 [plus or minus] cosh
                 x)[superscript -m] / 185 \\
                 7.7: Integrands Involving sinh(ax)cosh[superscript -n]
                 x or cosh(ax)sinh[superscript -n] x / 185 \\
                 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d)
                 / 186 \\
                 7.9: Integrands Involving tanh kx and coth kx / 188 \\
                 7.10: Integrands Involving (a + bx)[superscript m] sinh
                 kx or (a + bx)[superscript m] cosh kx / 189 \\
                 8: Indefinite Integrals Involving Inverse Hyperbolic
                 Functions \\
                 8.1: Basic Results / 191 \\
                 8.2: Integrands Involving x[superscript -n]
                 arcsinh(x/a) or x[superscript -n] arccosh(x/a) / 193
                 \\
                 8.3: Integrands Involving x[superscript n] arctanh(x/a)
                 or x[superscript n] arccoth(x/a) / 194 \\
                 8.4: Integrands Involving x[superscript -n]
                 arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195
                 \\
                 9: Indefinite Integrals of Trigonometric Functions \\
                 9.1: Basic Results / 197 \\
                 9.2: Integrands Involving Powers of x and Powers of sin
                 x or cos x / 197 \\
                 9.3: Integrands Involving tan x and/or cot x / 205 \\
                 9.4: Integrands Involving sin x and cos x / 207 \\
                 9.5: Integrands Involving Sines and Cosines with Linear
                 Arguments and Powers of x / 211 \\
                 10: Indefinite Integrals of Inverse Trigonometric
                 Functions \\
                 10.1: Integrands Involving Powers of x and Powers of
                 Inverse Trigonometric Functions 215 --. 11: Gamma,
                 Beta, Pi, and Psi Functions \\
                 11.1: Euler Integral and Limit and Infinite Product
                 Representations for [Gamma] (x) / 221 \\
                 12: Elliptic Integrals and Functions \\
                 12.1: Elliptic Integrals / 229 \\
                 12.2: Jacobian Elliptic Functions / 235 \\
                 12.3: Derivatives and Integrals / 237 \\
                 12.4: Inverse Jacobian Elliptic Functions / 237 \\
                 13: Probability Integrals and the Error Function \\
                 13.1: Normal Distribution / 239 \\
                 13.2: Error Function / 242 \\
                 14: Fresnel Integrals, Sine and Cosine Integrals \\
                 14.1: Definitions, Series Representations, and Values
                 at Infinity / 245 \\
                 14.2: Definitions, Series Representations, and Values
                 at Infinity / 247 \\
                 15: Definite Integrals \\
                 15.1: Integrands Involving Powers of x / 249 \\
                 15.2: Integrands Involving Trigonometric Functions 251
                 \\
                 15.3: Integrands Involving the Exponential Function 254
                 \\
                 15.4: Integrands Involving the Hyperbolic Function 256
                 \\
                 15.5: Integrands Involving the Logarithmic Function 256
                 \\
                 16: Different Forms of Fourier Series \\
                 16.1: Fourier Series for f(x) on -[pi] [less than or
                 equal] x [less than or equal] [pi] / 257 \\
                 16.2: Fourier Series for f(x) on -L [less than or
                 equal] x [less than or equal] L / 258 \\
                 16.3: Fourier Series for f(x) on a [less than or equal]
                 x [less than or equal] b / 258 \\
                 16.4: Half-Range Fourier Cosine Series for f(x) on 0
                 [less than or equal] x [less than or equal] [pi] 259
                 \\
                 16.5: Half-Range Fourier Cosine Series for f(x) on 0
                 [less than or equal] x [less than or equal] L / 259 \\
                 16.6: Half-Range Fourier Sine Series for f(x) on 0
                 [less than or equal] x [less than or equal] [pi] 260
                 \\
                 16.7: Half-Range Fourier Sine Series for f(x) on 0
                 [less than or equal] x [less than or equal] L / 260 \\
                 16.8: Complex (Exponential) Fourier Series for f(x) on
                 -[pi] [less than or equal] x [less than or equal] [pi]
                 / 260 \\
                 16.9: Complex (Exponential) Fourier Series for f(x) on
                 -L [less than or equal] x [less than or equal] L 261
                 \\
                 16.10: Representative Examples of Fourier Series 261
                 \\
                 16.11: Fourier Series and Discontinuous Functions 265
                 \\
                 17: Bessel Functions \\
                 17.1: Bessel's Differential Equation / 269 \\
                 17.2: Series Expansions for J[subscript v](x) and
                 Y[subscript v](x) / 270 \\
                 17.3: Bessel Functions of Fractional Order / 272 \\
                 17.4: Asymptotic Representations for Bessel Functions /
                 273 \\
                 17.5: Zeros of Bessel Functions / 273 \\
                 17.6: Bessel's Modified Equation / 274 \\
                 17.7: Series Expansions for I[subscript v](x) and
                 K[subscript v](x) / 276 \\
                 17.8: Modified Bessel Functions of Fractional Order 277
                 \\
                 17.9: Asymptotic Representations of Modified Bessel
                 Functions / 278 \\
                 17.10: Relationships between Bessel Functions / 278 \\
                 17.11: Integral Representations of J[subscript n](x),
                 I[subscript n](x), and K[subscript n](x) / 281 \\
                 17.12: Indefinite Integrals of Bessel Functions / 281
                 \\
                 17.13: Definite Integrals Involving Bessel Functions /
                 282 \\
                 17.14: Spherical Bessel Functions / 283 \\
                 18: Orthogonal Polynomials \\
                 18.2: Legendre Polynomials P[subscript n](x) / 286 \\
                 18.3: Chebyshev Polynomials T[subscript n](x) and
                 U[subscript n](x) / 290 \\
                 18.4: Laguerre Polynomials L[subscript n](x) / 294 \\
                 18.5: Hermite Polynomials H[subscript n](x) / 296 \\
                 19: Laplace Transformation \\
                 20: Fourier Transforms \\
                 21: Numerical Integration \\
                 21.1: Classical Methods / 315 \\
                 22: Solutions of Standard Ordinary Differential
                 Equations \\
                 22.2: Separation of Variables / 323 \\
                 22.3: Linear First-Order Equations / 323 \\
                 22.4: Bernoulli's Equation / 324 \\
                 22.5: Exact Equations / 325 \\
                 22.6: Homogeneous Equations / 325 \\
                 22.7: Linear Differential Equations / 326 \\
                 22.8: Constant Coefficient Linear Differential
                 Equations--Homogeneous Case / 327 \\
                 22.9: Linear Homogeneous Second-Order Equation / 330
                 \\
                 22.10: Constant Coefficient Linear Differential
                 Equations--Inhomogeneous Case / 331 \\
                 22.11: Linear Inhomogeneous Second-Order Equation 333
                 \\
                 22.12: Determination of Particular Integrals by the
                 Method of- Undetermined Coefficients / 334 \\
                 22.13: Cauchy-Euler Equation / 336 \\
                 22.14: Legendre's Equation / 337 \\
                 22.15: Bessel's Equations / 337 \\
                 22.16: Power Series and Frobenius Methods / 339 \\
                 22.17: Hypergeometric Equation / 344 \\
                 22.18: Numerical Methods / 345 \\
                 23: Vector Analysis \\
                 23.1: Scalars and Vectors / 353 \\
                 23.2: Scalar Products / 358 \\
                 23.3: Vector Products / 359 \\
                 23.4: Triple Products / 360 \\
                 23.5: Products of Four Vectors / 361 \\
                 23.6: Derivatives of Vector Functions of a Scalar t 361
                 \\
                 23.7: Derivatives of Vector Functions of Several Scalar
                 Variables / 362 \\
                 23.8: Integrals of Vector Functions of a Scalar
                 Variable t / 363 \\
                 23.9: Line Integrals / 364 \\
                 23.10: Vector Integral Theorems / 366 \\
                 23.11: A Vector Rate of Change Theorem / 368 \\
                 23.12: Useful Vector Identities and Results / 368 \\
                 24: Systems of Orthogonal Coordinates \\
                 24.1: Curvilinear Coordinates / 369 \\
                 24.2: Vector Operators in Orthogonal Coordinates 371
                 \\
                 24.3: Systems of Orthogonal Coordinates / 371 \\
                 25: Partial Differential Equations and Special
                 Functions \\
                 25.1: Fundamental Ideas / 381 \\
                 25.2: Method of Separation of Variables / 385 \\
                 25.3: Sturm--Liouville Problem and Special Functions
                 387 \\
                 25.4: A First-Order System and the Wave Equation 390
                 \\
                 25.5: Conservation Equations (Laws) / 391 \\
                 25.6: Method of Characteristics / 392 \\
                 25.7: Discontinuous Solutions (Shocks) / 396 \\
                 25.8: Similarity Solutions / 398 \\
                 25.9: Burgers's Equation, the KdV Equation, and the
                 KdVB Equation / 400 \\
                 26: Z-Transform \\
                 26.1: Z-Transform and Transform Pairs / 403 \\
                 27: Numerical Approximation \\
                 27.2: Economization of Series / 411 \\
                 27.3: Pade Approximation / 413 \\
                 27.4: Finite Difference Approximations to Ordinary and
                 Partial Derivatives / 415",
}


bibtype: article
filename: elefunt.bib
label: Kilbas:2000:CFI
author: A. A. Kilbas and J. J. Trujillo
title: Computation of fractional integrals via functions of hypergeometric and Bessel type
journal: j-J-COMPUT-APPL-MATH
volume: 118
number: 1--2
pages: 223--239
day: 1
month: jun
monthnumber: 6
year: 2000
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:43:35 MST 2017
bibtimestamp: 2017.02.25 12:43:35 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700002910
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: A. A. Kilbas and J. J. Trujillo
rawtitle: Computation of fractional integrals via functions of hypergeometric and {Bessel} type
entry:
@Article{Kilbas:2000:CFI,
  author =       "A. A. Kilbas and J. J. Trujillo",
  title =        "Computation of fractional integrals via functions of
                 hypergeometric and {Bessel} type",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "118",
  number =       "1--2",
  pages =        "223--239",
  day =          "1",
  month =        jun,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:43:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700002910",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lefevre:2000:CRF
author: V. D. Lefevre and J.-M. Muller
booktitle: Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, 2000
title: Correctly rounded functions for better arithmetic
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 875--878
year: 2000
bibdate: Sat Jul 16 11:25:05 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 11:25:05 MDT
acknowledgement: ack-nhfb
rawauthor: V. D. Lefevre and J.-M. Muller
rawbooktitle: Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, 2000
rawtitle: Correctly rounded functions for better arithmetic
entry:
@InProceedings{Lefevre:2000:CRF,
  author =       "V. D. Lefevre and J.-M. Muller",
  booktitle =    "Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000",
  title =        "Correctly rounded functions for better arithmetic",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "875--878",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The IEEE 754 standard for floating-point arithmetic
                 requires that the four arithmetic operations and the
                 square root should be correctly rounded. This has
                 improved the accuracy, reliability and portability of
                 numerical software. Unfortunately, such \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Lopez:2000:AES
author: Jose L. Lopez
title: Asymptotic Expansions of Symmetric Standard Elliptic Integrals
journal: j-SIAM-J-MATH-ANA
volume: 31
number: 4
pages: 754--775
year: 2000
CODEN: SJMAAH
DOI: https://doi.org/10.1137/S0036141099351176
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
bibdate: Fri Oct 27 08:17:04 MDT 2000
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SIMA/31/4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2000.10.27 08:17:04 MDT
URL: http://epubs.siam.org/sam-bin/dbq/article/35117
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: Jos{\'e} L. L{\'o}pez
rawtitle: Asymptotic Expansions of Symmetric Standard Elliptic Integrals
entry:
@Article{Lopez:2000:AES,
  author =       "Jos{\'e} L. L{\'o}pez",
  title =        "Asymptotic Expansions of Symmetric Standard Elliptic
                 Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "31",
  number =       "4",
  pages =        "754--775",
  year =         "2000",
  CODEN =        "SJMAAH",
  DOI =          "https://doi.org/10.1137/S0036141099351176",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Fri Oct 27 08:17:04 MDT 2000",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/31/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/35117",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lozier:2000:DPN
author: Daniel W. Lozier
title: The DLMF Project: a New Initiative in Classical Special Functions
crossref: Dunkl:2000:PIW
pages: 207--220
year: 2000
bibdate: Fri Jul 09 06:31:32 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:31:32 ???
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier
rawtitle: The {DLMF Project}: a New Initiative in Classical Special Functions
entry:
@InProceedings{Lozier:2000:DPN,
  author =       "Daniel W. Lozier",
  title =        "The {DLMF Project}: a New Initiative in Classical
                 Special Functions",
  crossref =     "Dunkl:2000:PIW",
  pages =        "207--220",
  year =         "2000",
  bibdate =      "Fri Jul 09 06:31:32 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Markstein:2000:IEF
author: Peter Markstein
title: IA-64 and elementary functions: speed and precision
publisher: pub-PH
address: pub-PH:adr
pages: xix + 298
year: 2000
ISBN: 0-13-018348-2 OR 0130183482
ISBN13: 978-0-13-018348-4 OR 9780130183484
LCCN: QA76.9.A73 M365 2000
bibdate: Fri Jan 5 08:00:52 MST 2001
bibtimestamp: 2001.01.05 08:00:52 MST
series: Hewlett--Packard professional books
URL: http://www.markstein.org/
keywords: IA-64 (computer architecture)
acknowledgement: ack-nhfb
rawauthor: Peter Markstein
rawtitle: {IA-64} and elementary functions: speed and precision
bibsource:
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/intel-ia-64.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/microchip.bib; University of California MELVYL catalog.

remark:
Besides recipes for accurate computation of elementary functions, this book also contains algorithms for the correctly-rounded computation of floating-point division and square-root, and of integer division, starting from low-precision reciprocal approximations. There is also a wealth of information on the tradeoffs between integer and floating-point instruction use in a pipelined parallel architecture.

TOC:
IA-64 Architecture New Architecture Objectives VLIW Memory Enhancements Software Pipelining Floating Point Enhancements Summary IA-64 Instructions And Registers Instructions Register Sets Accessing Memory Assembly Language Problems Increasing Instruction Level Parallelism Branching Speculation Problems Floating Point Architecture Floating Point Status Register Precision Fused Multiply-Add Division and Square Root Assists Floating Comparisons Communication between Floating Point and General Purpose Registers Fixed Point Multiplication SIMD Arithmetic Problems Programming For IA-64 Compiler Options Pragmas Floating Point Data Types In-Line Assembly The fenv.h Header Extended Examples Quad Precision Problems Computation of Elementary Functions Mathematical Preliminaries Floating Point Approximation and Error Analysis The Exclusion Theorem Ulps Problems Approximation Of Functions Taylor Series Lagrangian Interpolation Chebychev Approximation Remez Approximation Practical Considerations Function Evaluation Table Construction Problems Division Approximations for the Reciprocal Computing the Quotient Division Using Only Final Precision Results Fast Variants of Division Remainder Integer Division An Implementation of Division Problems Square Root Approximations Rounding the Square Root Computing the Square Root Calculating the Reciprocal Square Root An Implementation of Square Root Problems Exponential Functions Definitions and Formulas Argument Reduction Error Containment Computing the Exponential The Function expm Problems Logarithmic Functions General Relations Argument Reductions Error Analysis The Function log1p Computing the Logarithm Problems The Power Function Definition Single Precision Double Precision Double-Extended Precision Quad Precision Computing the Power Function Problems Trigonometric Functions Formulas and Identities Argument Reduction Error Analysis Computing the Trigonometric Functions Problems Inverse Sine And Cosine Definitions and Formulas Argument Reduction Error Analysis Computing the arcsin Problems Inverse Tangent Functions Definitions and Formulas Argument Reduction Error Analysis Computing the arctan Problems Hyperbolic Functions Definitions and Formulas Argument Reduction Error Analysis Computing the Hyperbolic Functions Problems Inverse Hyperbolic Functions Definitions and Formulas. arcsinh. arccosh. arctanh Problems Odds And Ends Correctly Rounded Functions Monotonicity Alternative Algorithms Testing New Architectural Directions Problems In-Line Assembly Solutions To Problems Bibliography Subject Index

rawTOC:
IA-64 Architecture \\ New Architecture Objectives \\ VLIW \\ Memory Enhancements \\ Software Pipelining \\ Floating Point Enhancements \\ Summary \\ IA-64 Instructions And Registers \\ Instructions \\ Register Sets \\ Accessing Memory \\ Assembly Language \\ Problems \\ Increasing Instruction Level Parallelism \\ Branching \\ Speculation \\ Problems \\ Floating Point Architecture \\ Floating Point Status Register \\ Precision \\ Fused Multiply-Add \\ Division and Square Root Assists \\ Floating Comparisons \\ Communication between Floating Point and General Purpose Registers \\ Fixed Point Multiplication \\ SIMD Arithmetic \\ Problems \\ Programming For IA-64 \\ Compiler Options \\ Pragmas \\ Floating Point Data Types \\ In-Line Assembly \\ The fenv.h Header \\ Extended Examples \\ Quad Precision \\ Problems \\ Computation of Elementary Functions \\ Mathematical Preliminaries \\ Floating Point \\ Approximation and Error Analysis \\ The Exclusion Theorem \\ Ulps \\ Problems \\ Approximation Of Functions \\ Taylor Series \\ Lagrangian Interpolation \\ Chebychev Approximation \\ Remez Approximation \\ Practical Considerations \\ Function Evaluation \\ Table Construction \\ Problems \\ Division \\ Approximations for the Reciprocal \\ Computing the Quotient \\ Division Using Only Final Precision Results \\ Fast Variants of Division \\ Remainder \\ Integer Division \\ An Implementation of Division \\ Problems \\ Square Root \\ Approximations \\ Rounding the Square Root \\ Computing the Square Root \\ Calculating the Reciprocal Square Root \\ An Implementation of Square Root \\ Problems \\ Exponential Functions \\ Definitions and Formulas \\ Argument Reduction \\ Error Containment \\ Computing the Exponential \\ The Function expm \\ Problems \\ Logarithmic Functions \\ General Relations \\ Argument Reductions \\ Error Analysis \\ The Function log1p \\ Computing the Logarithm \\ Problems \\ The Power Function \\ Definition \\ Single Precision \\ Double Precision \\ Double-Extended Precision \\ Quad Precision \\ Computing the Power Function \\ Problems \\ Trigonometric Functions \\ Formulas and Identities \\ Argument Reduction \\ Error Analysis \\ Computing the Trigonometric Functions \\ Problems \\ Inverse Sine And Cosine \\ Definitions and Formulas \\ Argument Reduction \\ Error Analysis \\ Computing the arcsin \\ Problems \\ Inverse Tangent Functions \\ Definitions and Formulas \\ Argument Reduction \\ Error Analysis \\ Computing the arctan \\ Problems \\ Hyperbolic Functions \\ Definitions and Formulas \\ Argument Reduction \\ Error Analysis \\ Computing the Hyperbolic Functions \\ Problems \\ Inverse Hyperbolic Functions \\ Definitions and Formulas. arcsinh. arccosh. arctanh \\ Problems \\ Odds And Ends \\ Correctly Rounded Functions \\ Monotonicity \\ Alternative Algorithms \\ Testing \\ New Architectural Directions \\ Problems \\ In-Line Assembly \\ Solutions To Problems \\ Bibliography \\ Subject Index

entry:
@Book{Markstein:2000:IEF,
  author =       "Peter Markstein",
  title =        "{IA-64} and elementary functions: speed and
                 precision",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xix + 298",
  year =         "2000",
  ISBN =         "0-13-018348-2",
  ISBN-13 =      "978-0-13-018348-4",
  LCCN =         "QA76.9.A73 M365 2000",
  bibdate =      "Fri Jan 5 08:00:52 MST 2001",
  bibsource =    "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/intel-ia-64.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib;
                 University of California MELVYL catalog.",
  series =       "Hewlett--Packard professional books",
  URL =          "http://www.markstein.org/",
  acknowledgement = ack-nhfb,
  keywords =     "IA-64 (computer architecture)",
  remark =       "Besides recipes for accurate computation of elementary
                 functions, this book also contains algorithms for the
                 correctly-rounded computation of floating-point
                 division and square-root, and of integer division,
                 starting from low-precision reciprocal approximations.
                 There is also a wealth of information on the tradeoffs
                 between integer and floating-point instruction use in a
                 pipelined parallel architecture.",
  tableofcontents = "IA-64 Architecture \\
                 New Architecture Objectives \\
                 VLIW \\
                 Memory Enhancements \\
                 Software Pipelining \\
                 Floating Point Enhancements \\
                 Summary \\
                 IA-64 Instructions And Registers \\
                 Instructions \\
                 Register Sets \\
                 Accessing Memory \\
                 Assembly Language \\
                 Problems \\
                 Increasing Instruction Level Parallelism \\
                 Branching \\
                 Speculation \\
                 Problems \\
                 Floating Point Architecture \\
                 Floating Point Status Register \\
                 Precision \\
                 Fused Multiply-Add \\
                 Division and Square Root Assists \\
                 Floating Comparisons \\
                 Communication between Floating Point and General
                 Purpose Registers \\
                 Fixed Point Multiplication \\
                 SIMD Arithmetic \\
                 Problems \\
                 Programming For IA-64 \\
                 Compiler Options \\
                 Pragmas \\
                 Floating Point Data Types \\
                 In-Line Assembly \\
                 The fenv.h Header \\
                 Extended Examples \\
                 Quad Precision \\
                 Problems \\
                 Computation of Elementary Functions \\
                 Mathematical Preliminaries \\
                 Floating Point \\
                 Approximation and Error Analysis \\
                 The Exclusion Theorem \\
                 Ulps \\
                 Problems \\
                 Approximation Of Functions \\
                 Taylor Series \\
                 Lagrangian Interpolation \\
                 Chebychev Approximation \\
                 Remez Approximation \\
                 Practical Considerations \\
                 Function Evaluation \\
                 Table Construction \\
                 Problems \\
                 Division \\
                 Approximations for the Reciprocal \\
                 Computing the Quotient \\
                 Division Using Only Final Precision Results \\
                 Fast Variants of Division \\
                 Remainder \\
                 Integer Division \\
                 An Implementation of Division \\
                 Problems \\
                 Square Root \\
                 Approximations \\
                 Rounding the Square Root \\
                 Computing the Square Root \\
                 Calculating the Reciprocal Square Root \\
                 An Implementation of Square Root \\
                 Problems \\
                 Exponential Functions \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Containment \\
                 Computing the Exponential \\
                 The Function expm \\
                 Problems \\
                 Logarithmic Functions \\
                 General Relations \\
                 Argument Reductions \\
                 Error Analysis \\
                 The Function log1p \\
                 Computing the Logarithm \\
                 Problems \\
                 The Power Function \\
                 Definition \\
                 Single Precision \\
                 Double Precision \\
                 Double-Extended Precision \\
                 Quad Precision \\
                 Computing the Power Function \\
                 Problems \\
                 Trigonometric Functions \\
                 Formulas and Identities \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the Trigonometric Functions \\
                 Problems \\
                 Inverse Sine And Cosine \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the arcsin \\
                 Problems \\
                 Inverse Tangent Functions \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the arctan \\
                 Problems \\
                 Hyperbolic Functions \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the Hyperbolic Functions \\
                 Problems \\
                 Inverse Hyperbolic Functions \\
                 Definitions and Formulas. arcsinh. arccosh. arctanh \\
                 Problems \\
                 Odds And Ends \\
                 Correctly Rounded Functions \\
                 Monotonicity \\
                 Alternative Algorithms \\
                 Testing \\
                 New Architectural Directions \\
                 Problems \\
                 In-Line Assembly \\
                 Solutions To Problems \\
                 Bibliography \\
                 Subject Index",
}


bibtype: article
filename: elefunt.bib
label: Paliouras:2000:FPP
author: V. Paliouras and K. Karagianni and T. Stouraitis
title: A floating-point processor for fast and accurate sine / cosine evaluation
journal: j-IEEE-TRANS-CIRCUITS-SYST-2
volume: 47
number: 5
pages: 441--451
month: may
monthnumber: 5
year: 2000
CODEN: ICSPE5
DOI: https://doi.org/10.1109/82.842112
ISSN: 1057-7130 (print), 1558-125X (electronic) OR 10577130 (print), 1558125X (electronic)
ISSNL: 1057-7130 OR 10577130
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Circuits and Systems. 2, Analog and Digital Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82
rawauthor: V. Paliouras and K. Karagianni and T. Stouraitis
rawtitle: A floating-point processor for fast and accurate sine\slash cosine evaluation
entry:
@Article{Paliouras:2000:FPP,
  author =       "V. Paliouras and K. Karagianni and T. Stouraitis",
  title =        "A floating-point processor for fast and accurate
                 sine\slash cosine evaluation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "47",
  number =       "5",
  pages =        "441--451",
  month =        may,
  year =         "2000",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.842112",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "A VLSI architecture for fast and accurate
                 floating-point sine/cosine evaluation is presented,
                 combining floating-point and simple fixed-point
                 arithmetic. The algorithm implemented by the
                 architecture is based on second order polynomial
                 interpolation \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Simon:2000:DCF
author: Marvin Kenneth Simon and Mohamed-Slim Alouini
title: Digital Communication over Fading Channels: a Unified Approach to Performance Analysis
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xix + 544
year: 2000
ISBN: 0-471-31779-9 OR 0471317799
ISBN13: 978-0-471-31779-1 OR 9780471317791
LCCN: TK5103.7 .S523 2000
bibdate: Sat Dec 16 17:34:06 MST 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.12.16 17:34:06 MST
series: Wiley series in telecommunications and signal processing
subject: Digital communications; Reliability; Mathematics; Radio; Transmitters and transmission; Fading
acknowledgement: ack-nhfb
authordates: 1939--
rawauthor: Marvin Kenneth Simon and Mohamed-Slim Alouini
rawtitle: Digital Communication over Fading Channels: a Unified Approach to Performance Analysis
URL:
http://www.loc.gov/catdir/bios/wiley043/99056352.html; http://www.loc.gov/catdir/description/wiley035/99056352.html; http://www.loc.gov/catdir/toc/onix06/99056352.html

TOC:
1.1: System Performance Measures 4 1.1.1: Average Signal-to-Noise Ratio 4 1.1.2: Outage Probability 5 1.1.3: Average Bit Error Probability 6 Chapter 2: Fading Channel Characterization and Modeling 15 2.1: Main Characteristics of Fading Channels 15 2.1.1: Envelope and Phase Fluctuations 15 2.1.2: Slow and Fast Fading 16 2.1.3: Frequency-Flat and Frequency-Selective Fading 16 2.2: Modeling of Flat Fading Channels 17 2.2.1: Multipath Fading 18 2.2.2: Log-Normal Shadowing 23 2.2.3: Composite Multipath/Shadowing 24 2.2.4: Combined (Time-Shared) Shadowed/Unshadowed Fading 25 2.3: Modeling of Frequency-Selective Fading Channels 26 Chapter 3: Types of Communication 31 3.1: Ideal Coherent Detection 31 3.1.1: Multiple Amplitude-Shift-Keying or Multiple Amplitude Modulation 33 3.1.2: Quadrature Amplitude-Shift-Keying or Quadrature Amplitude Modulation 34 3.1.3: M-ary Phase-Shift-Keying 35 3.1.4: Differentially Encoded M-ary Phase-Shift-Keying 39 3.1.5: Offset QPSK or Staggered QPSK 41 3.1.6: M-ary Frequency-Shift-Keying 43 3.1.7: Minimum-Shift-Keying 45 3.2: Nonideal Coherent Detection 47 3.3: Noncoherent Detection 53 3.4: Partially Coherent Detection 55 3.4.1: Conventional Detection: One-Symbol Observation 55 3.4.2: Multiple Symbol Detection 57 3.5: Differentially Coherent Detection 59 3.5.1: M-ary Differential Phase Shift Keying 59 3.5.2: [pi]/4-Differential QPSK 65 Part 2: Mathematical Tools Chapter 4: Alternative Representations of Classical Functions 69 4.1: Gaussian $Q$-Function 70 4.1.1: One-Dimensional Case 70 4.1.2: Two-Dimensional Case 72 4.2: Marcum $Q$-Function 74 4.2.1: First-Order Marcum $Q$-Function 74 4.2.2: Generalized ($m$th-Order) Marcum $Q$-Function 81 4.3: Other Functions 90 Appendix 4A: Derivation of Eq. (4.2) 95 Chapter 5: Useful Expressions for Evaluating Average Error Probability Performance 99 5.1: Integrals Involving the Gaussian $Q$-Function 99 5.1.1: Rayleigh Fading Channel 101 5.1.2: Nakagami-q (Hoyt) Fading Channel 101 5.1.3: Nakagami-n (Rice) Fading Channel 102 5.1.4: Nakagami-m Fading Channel 102 5.1.5: Log-Normal Shadowing Channel 104 5.1.6: Composite Log-Normal Shadowing/Nakagami-m Fading Channel 104 5.2: Integrals Involving the Marcum $Q$-Function 107 5.2.1: Rayleigh Fading Channel 108 5.2.2: Nakagami-q (Hoyt) Fading Channel 109 5.2.3: Nakagami-n (Rice) Fading Channel 109 5.2.4: Nakagami-m Fading Channel 109 5.2.5: Log-Normal Shadowing Channel 109 5.2.6: Composite Log-Normal Shadowing/Nakagami-m Fading Channel 110 5.3: Integrals Involving the Incomplete Gamma Function 111 5.3.1: Rayleigh Fading Channel 112 5.3.2: Nakagami-q (Hoyt) Fading Channel 112 5.3.3: Nakagami-n (Rice) Fading Channel 112 5.3.4: Nakagami-m Fading Channel 113 5.3.5: Log-Normal Shadowing Channel 114 5.3.6: Composite Log-Normal Shadowing/Nakagami-m Fading Channel 114 5.4: Integrals Involving Other Functions 114 5.4.1: M-PSK Error Probability Integral 114 5.4.2: Arbitrary Two-Dimensional Signal Constellation Error Probability Integral 116 5.4.3: Integer Powers of the Gaussian $Q$-Function 117 5.4.4: Integer Powers of M-PSK Error Probability Integrals 121 Appendix 5A: Evaluation of Definite Integrals Associated with Rayleigh and Nakagami-$m$ Fading 124 Chapter 6: New Representations of Some PDF's and CDF's for Correlative Fading Applications 141 6.1: Bivariate Rayleigh PDF and CDF 142 6.2: PDF and CDF for Maximum of Two Rayleigh Random Variables 146 6.3: PDF and CDF for Maximum of Two Nakagami-m Random Variables 149 Part 3: Optimum Reception and Performance Evaluation Chapter 7: Optimum Receivers for Fading Channels 157 7.1: Case of Known Amplitudes, Phases, and Delays: Coherent, Detection 159 7.2: Case of Known Phases and Delays, Unknown Amplitudes 163 7.2.1: Rayleigh Fading 163 7.2.2: Nakagami-m Fading 164 7.3: Case of Known Amplitudes and Delays, Unknown Phases 166 7.4: Case of Known Delays and Unknown Amplitudes and Phases 168 7.4.1: One-Symbol Observation: Noncoherent Detection 168 7.4.2: Two-Symbol Observation: Conventional Differentially Coherent Detection 181 7.4.3: N-Symbol Observation: Multiple Symbol Differentially Coherent Detection 186 7.5: Case of Unknown Amplitudes, Phases, and Delays 188 7.5.1: One-Symbol Observation: Noncoherent Detection 188 7.5.2: Two-Symbol Observation: Conventional Differentially Coherent Detection 190 Chapter 8: Performance of Single Channel Receives 193 8.1: Performance Over the AWGN Channel 193 8.1.1: Ideal Coherent Detection 194 8.1.2: Nonideal Coherent Detection 206 8.1.3: Noncoherent Detection 209 8.1.4: Partially Coherent Detection 210 8.1.5: Differentially Coherent Detection 213 8.1.6: Generic Results for Binary Signaling 218 8.2: Performance Over Fading Channels 219 8.2.1: Ideal Coherent Detection 220 8.2.2: Nonideal Coherent Detection 234 8.2.3: Noncoherent Detection 239 8.2.4: Partially Coherent Detection 242 8.2.5: Differentially Coherent Detection 243 Appendix 8A: Stein's Unified Analysis of the Error Probability Performance of Certain Communication Systems 253 Chapter 9: Performance of Multichannel Receivers 259 9.1: Diversity Combining 260 9.1.1: Diversity Concept 260 9.1.2: Mathematical Modeling 260 9.1.3: Brief Survey of Diversity Combining Techniques 261 9.1.4: Complexity-Performance Trade-offs 264 9.2: Maximal-Ratio Combining 265 9.2.1: Receiver Structure 265 9.2.2: PDF-Based Approach 267 9.2.3: MGF-Based Approach 268 9.2.4: Bounds and Asymptotic SER Expressions 275 9.3: Coherent Equal Gain Combining 278 9.3.1: Receiver Structure 279 9.3.2: Average Output SNR 279 9.3.3: Exact Error Rate Analysis 281 9.3.4: Approximate Error Rate Analysis 288 9.3.5: Asymptotic Error Rate Analysis 289 9.4: Noncoherent Equal-Gain Combining 290 9.4.1: DPSK, DQPSK, and BFSK: Exact and Bounds 290 9.4.2: M-ary Orthogonal FSK 304 9.5: Outage Probability Performance 311 9.5.1: MRC and Noncoherent EGC 312 9.5.2: Coherent EGC 313 9.5.3: Numerical Examples 314 9.6: Impact of Fading Correlation 316 9.6.1: Model A: Two Correlated Branches with Nonidentical Fading 320 9.6.2: Model B: D Identically Distributed Branches with Constant Correlation 323 9.6.3: Model C: D Identically Distributed Branches with Exponential Correlation 324 9.6.4: Model D: D Nonidentically Distributed Branches with Arbitrary Correlation 325 9.6.5: Numerical Examples 329 9.7: Selection Combining 333 9.7.1: MGF of Output SNR 335 9.7.2: Average Output SNR 336 9.7.3: Outage Probability 338 9.7.4: Average Probability of Error 340 9.8: Switched Diversity 348 9.8.1: Performance of SSC over Independent Identically Distributed Branches 348 9.8.2: Effect of Branch Unbalance 362 9.8.3: Effect of Branch Correlation 366 9.9: Performance in the Presence of Outdated or Imperfect Channel Estimates 370 9.9.1: Maximal-Ratio Combining 370 9.9.2: Noncoherent EGC over Rician Fast Fading 371 9.9.3: Selection Combining 373 9.9.4: Switched Diversity 374 9.9.5: Numerical Results 377 9.10: Hybrid Diversity Schemes 378 9.10.1: Generalized Selection Combining 378 9.10.2: Generalized Switched Diversity 403 9.10.3: Two-Dimensional Diversity Schemes 408 Appendix 9A: Alternative Forms of the Bit Error Probability for a Decision Statistic that is a Quadratic Form of Complex Gaussian Random Variables 421 Appendix 9B: Simple Numerical Techniques for thee Inversion of the Laplace Transform of Cumulative Distribution Functions 427 9B.1: Euler Summation-Based Technique 427 9B.2: Gauss-Chebyshev Quadrature-Based Technique 428 Appendix 9C: Proof of Theorem 1 430 Appendix 9D: Direct Proof of Eq. (9.331) 431 Appendix 9E: Special Definite Integrals 432 Part 4: Application in Practical Communication Systems Chapter 10: Optimum Combining: A Diversity Technique for Communication Over Fading Channels in the Presence of Interference 437 10.1: Performance of Optimum Combining Receivers 438 10.1.1: Single Interferer, Independent Identically Distributed Fading 438 10.1.2: Multiple Interferers, Independent Identically Distributed Fading 454 10.1.3: Comparison with Results for MRC in the Presence of Interference 466 Chapter 11: Direct-Sequence Code-Division Multiple Access 473 11.1: Single-Carrier DS-CDMA Systems 474 11.1.1: System and Channel Models 474 11.1.2: Performance Analysis 477 11.2: Multicarrier DS-CDMA Systems 479 11.2.1: System and Channel Models 480 11.2.2: Performance Analysis 483 11.2.3: Numerical Examples 489 Part 5: Further Extensions Chapter 12: Coded Communication Over Fading Channels 497 12.1: Coherent Detection 499 12.1.1: System Model 499 12.1.2: Evaluation of Pairwise Error Probability 502 12.1.3: Transfer Function Bound on Average Bit Error Probability 510 12.1.4: Alternative Formulation of the Transfer Function Bound 513 12.2: Differentially Coherent Detection 520 12.2.1: System Model 520 12.2.2: Performance Evaluation 522 12.3: Numerical Results: Comparison of the True Upper Bounds and Union-Chernoff Bounds 526 Appendix 12A: Evaluation of a Moment Generating Function Associated with Differential Detection of M-PSK Sequences 532

rawTOC:
1.1: System Performance Measures 4 \\ 1.1.1: Average Signal-to-Noise Ratio 4 \\ 1.1.2: Outage Probability 5 \\ 1.1.3: Average Bit Error Probability 6 \\ Chapter 2: Fading Channel Characterization and Modeling 15 \\ 2.1: Main Characteristics of Fading Channels 15 \\ 2.1.1: Envelope and Phase Fluctuations 15 \\ 2.1.2: Slow and Fast Fading 16 \\ 2.1.3: Frequency-Flat and Frequency-Selective Fading 16 \\ 2.2: Modeling of Flat Fading Channels 17 \\ 2.2.1: Multipath Fading 18 \\ 2.2.2: Log-Normal Shadowing 23 \\ 2.2.3: Composite Multipath/Shadowing 24 \\ 2.2.4: Combined (Time-Shared) Shadowed/Unshadowed Fading 25 \\ 2.3: Modeling of Frequency-Selective Fading Channels 26 \\ Chapter 3: Types of Communication 31 \\ 3.1: Ideal Coherent Detection 31 \\ 3.1.1: Multiple Amplitude-Shift-Keying or Multiple Amplitude Modulation 33 \\ 3.1.2: Quadrature Amplitude-Shift-Keying or Quadrature Amplitude Modulation 34 \\ 3.1.3: M-ary Phase-Shift-Keying 35 \\ 3.1.4: Differentially Encoded M-ary Phase-Shift-Keying 39 \\ 3.1.5: Offset QPSK or Staggered QPSK 41 \\ 3.1.6: M-ary Frequency-Shift-Keying 43 \\ 3.1.7: Minimum-Shift-Keying 45 \\ 3.2: Nonideal Coherent Detection 47 \\ 3.3: Noncoherent Detection 53 \\ 3.4: Partially Coherent Detection 55 \\ 3.4.1: Conventional Detection: One-Symbol Observation 55 \\ 3.4.2: Multiple Symbol Detection 57 \\ 3.5: Differentially Coherent Detection 59 \\ 3.5.1: M-ary Differential Phase Shift Keying 59 \\ 3.5.2: [pi]/4-Differential QPSK 65 \\ Part 2: Mathematical Tools \\ Chapter 4: Alternative Representations of Classical Functions 69 \\ 4.1: Gaussian $Q$-Function 70 \\ 4.1.1: One-Dimensional Case 70 \\ 4.1.2: Two-Dimensional Case 72 \\ 4.2: Marcum $Q$-Function 74 \\ 4.2.1: First-Order Marcum $Q$-Function 74 \\ 4.2.2: Generalized ($m$th-Order) Marcum $Q$-Function 81 \\ 4.3: Other Functions 90 \\ Appendix 4A: Derivation of Eq. (4.2) 95 \\ Chapter 5: Useful Expressions for Evaluating Average Error Probability Performance 99 \\ 5.1: Integrals Involving the Gaussian $Q$-Function 99 \\ 5.1.1: Rayleigh Fading Channel 101 \\ 5.1.2: Nakagami-q (Hoyt) Fading Channel 101 \\ 5.1.3: Nakagami-n (Rice) Fading Channel 102 \\ 5.1.4: Nakagami-m Fading Channel 102 \\ 5.1.5: Log-Normal Shadowing Channel 104 \\ 5.1.6: Composite Log-Normal Shadowing/Nakagami-m Fading Channel 104 \\ 5.2: Integrals Involving the Marcum $Q$-Function 107 \\ 5.2.1: Rayleigh Fading Channel 108 \\ 5.2.2: Nakagami-q (Hoyt) Fading Channel 109 \\ 5.2.3: Nakagami-n (Rice) Fading Channel 109 \\ 5.2.4: Nakagami-m Fading Channel 109 \\ 5.2.5: Log-Normal Shadowing Channel 109 \\ 5.2.6: Composite Log-Normal Shadowing/Nakagami-m Fading Channel 110 \\ 5.3: Integrals Involving the Incomplete Gamma Function 111 \\ 5.3.1: Rayleigh Fading Channel 112 \\ 5.3.2: Nakagami-q (Hoyt) Fading Channel 112 \\ 5.3.3: Nakagami-n (Rice) Fading Channel 112 \\ 5.3.4: Nakagami-m Fading Channel 113 \\ 5.3.5: Log-Normal Shadowing Channel 114 \\ 5.3.6: Composite Log-Normal Shadowing/Nakagami-m Fading Channel 114 \\ 5.4: Integrals Involving Other Functions 114 \\ 5.4.1: M-PSK Error Probability Integral 114 \\ 5.4.2: Arbitrary Two-Dimensional Signal Constellation Error Probability Integral 116 \\ 5.4.3: Integer Powers of the Gaussian $Q$-Function 117 \\ 5.4.4: Integer Powers of M-PSK Error Probability Integrals 121 \\ Appendix 5A: Evaluation of Definite Integrals Associated with Rayleigh and Nakagami-$m$ Fading 124 \\ Chapter 6: New Representations of Some PDF's and CDF's for Correlative Fading Applications 141 \\ 6.1: Bivariate Rayleigh PDF and CDF 142 \\ 6.2: PDF and CDF for Maximum of Two Rayleigh Random Variables 146 \\ 6.3: PDF and CDF for Maximum of Two Nakagami-m Random Variables 149 \\ Part 3: Optimum Reception and Performance Evaluation \\ Chapter 7: Optimum Receivers for Fading Channels 157 \\ 7.1: Case of Known Amplitudes, Phases, and Delays: Coherent, Detection 159 \\ 7.2: Case of Known Phases and Delays, Unknown Amplitudes 163 \\ 7.2.1: Rayleigh Fading 163 \\ 7.2.2: Nakagami-m Fading 164 \\ 7.3: Case of Known Amplitudes and Delays, Unknown Phases 166 \\ 7.4: Case of Known Delays and Unknown Amplitudes and Phases 168 \\ 7.4.1: One-Symbol Observation: Noncoherent Detection 168 \\ 7.4.2: Two-Symbol Observation: Conventional Differentially Coherent Detection 181 \\ 7.4.3: N-Symbol Observation: Multiple Symbol Differentially Coherent Detection 186 \\ 7.5: Case of Unknown Amplitudes, Phases, and Delays 188 \\ 7.5.1: One-Symbol Observation: Noncoherent Detection 188 \\ 7.5.2: Two-Symbol Observation: Conventional Differentially Coherent Detection 190 \\ Chapter 8: Performance of Single Channel Receives 193 \\ 8.1: Performance Over the AWGN Channel 193 \\ 8.1.1: Ideal Coherent Detection 194 \\ 8.1.2: Nonideal Coherent Detection 206 \\ 8.1.3: Noncoherent Detection 209 \\ 8.1.4: Partially Coherent Detection 210 \\ 8.1.5: Differentially Coherent Detection 213 \\ 8.1.6: Generic Results for Binary Signaling 218 \\ 8.2: Performance Over Fading Channels 219 \\ 8.2.1: Ideal Coherent Detection 220 \\ 8.2.2: Nonideal Coherent Detection 234 \\ 8.2.3: Noncoherent Detection 239 \\ 8.2.4: Partially Coherent Detection 242 \\ 8.2.5: Differentially Coherent Detection 243 \\ Appendix 8A: Stein's Unified Analysis of the Error Probability Performance of Certain Communication Systems 253 \\ Chapter 9: Performance of Multichannel Receivers 259 \\ 9.1: Diversity Combining 260 \\ 9.1.1: Diversity Concept 260 \\ 9.1.2: Mathematical Modeling 260 \\ 9.1.3: Brief Survey of Diversity Combining Techniques 261 \\ 9.1.4: Complexity-Performance Trade-offs 264 \\ 9.2: Maximal-Ratio Combining 265 \\ 9.2.1: Receiver Structure 265 \\ 9.2.2: PDF-Based Approach 267 \\ 9.2.3: MGF-Based Approach 268 \\ 9.2.4: Bounds and Asymptotic SER Expressions 275 \\ 9.3: Coherent Equal Gain Combining 278 \\ 9.3.1: Receiver Structure 279 \\ 9.3.2: Average Output SNR 279 \\ 9.3.3: Exact Error Rate Analysis 281 \\ 9.3.4: Approximate Error Rate Analysis 288 \\ 9.3.5: Asymptotic Error Rate Analysis 289 \\ 9.4: Noncoherent Equal-Gain Combining 290 \\ 9.4.1: DPSK, DQPSK, and BFSK: Exact and Bounds 290 \\ 9.4.2: M-ary Orthogonal FSK 304 \\ 9.5: Outage Probability Performance 311 \\ 9.5.1: MRC and Noncoherent EGC 312 \\ 9.5.2: Coherent EGC 313 \\ 9.5.3: Numerical Examples 314 \\ 9.6: Impact of Fading Correlation 316 \\ 9.6.1: Model A: Two Correlated Branches with Nonidentical Fading 320 \\ 9.6.2: Model B: D Identically Distributed Branches with Constant Correlation 323 \\ 9.6.3: Model C: D Identically Distributed Branches with Exponential Correlation 324 \\ 9.6.4: Model D: D Nonidentically Distributed Branches with Arbitrary Correlation 325 \\ 9.6.5: Numerical Examples 329 \\ 9.7: Selection Combining 333 \\ 9.7.1: MGF of Output SNR 335 \\ 9.7.2: Average Output SNR 336 \\ 9.7.3: Outage Probability 338 \\ 9.7.4: Average Probability of Error 340 \\ 9.8: Switched Diversity 348 \\ 9.8.1: Performance of SSC over Independent Identically Distributed Branches 348 \\ 9.8.2: Effect of Branch Unbalance 362 \\ 9.8.3: Effect of Branch Correlation 366 \\ 9.9: Performance in the Presence of Outdated or Imperfect Channel Estimates 370 \\ 9.9.1: Maximal-Ratio Combining 370 \\ 9.9.2: Noncoherent EGC over Rician Fast Fading 371 \\ 9.9.3: Selection Combining 373 \\ 9.9.4: Switched Diversity 374 \\ 9.9.5: Numerical Results 377 \\ 9.10: Hybrid Diversity Schemes 378 \\ 9.10.1: Generalized Selection Combining 378 \\ 9.10.2: Generalized Switched Diversity 403 \\ 9.10.3: Two-Dimensional Diversity Schemes 408 \\ Appendix 9A: Alternative Forms of the Bit Error Probability for a Decision Statistic that is a Quadratic Form of Complex Gaussian Random Variables 421 \\ Appendix 9B: Simple Numerical Techniques for thee Inversion of the Laplace Transform of Cumulative Distribution Functions 427 \\ 9B.1: Euler Summation-Based Technique 427 \\ 9B.2: Gauss-Chebyshev Quadrature-Based Technique 428 \\ Appendix 9C: Proof of Theorem 1 430 \\ Appendix 9D: Direct Proof of Eq. (9.331) 431 \\ Appendix 9E: Special Definite Integrals 432 \\ Part 4: Application in Practical Communication Systems \\ Chapter 10: Optimum Combining: A Diversity Technique for Communication Over Fading Channels in the Presence of Interference 437 \\ 10.1: Performance of Optimum Combining Receivers 438 \\ 10.1.1: Single Interferer, Independent Identically Distributed Fading 438 \\ 10.1.2: Multiple Interferers, Independent Identically Distributed Fading 454 \\ 10.1.3: Comparison with Results for MRC in the Presence of Interference 466 \\ Chapter 11: Direct-Sequence Code-Division Multiple Access 473 \\ 11.1: Single-Carrier DS-CDMA Systems 474 \\ 11.1.1: System and Channel Models 474 \\ 11.1.2: Performance Analysis 477 \\ 11.2: Multicarrier DS-CDMA Systems 479 \\ 11.2.1: System and Channel Models 480 \\ 11.2.2: Performance Analysis 483 \\ 11.2.3: Numerical Examples 489 \\ Part 5: Further Extensions \\ Chapter 12: Coded Communication Over Fading Channels 497 \\ 12.1: Coherent Detection 499 \\ 12.1.1: System Model 499 \\ 12.1.2: Evaluation of Pairwise Error Probability 502 \\ 12.1.3: Transfer Function Bound on Average Bit Error Probability 510 \\ 12.1.4: Alternative Formulation of the Transfer Function Bound 513 \\ 12.2: Differentially Coherent Detection 520 \\ 12.2.1: System Model 520 \\ 12.2.2: Performance Evaluation 522 \\ 12.3: Numerical Results: Comparison of the True Upper Bounds and Union-Chernoff Bounds 526 \\ Appendix 12A: Evaluation of a Moment Generating Function Associated with Differential Detection of M-PSK Sequences 532

entry:
@Book{Simon:2000:DCF,
  author =       "Marvin Kenneth Simon and Mohamed-Slim Alouini",
  title =        "Digital Communication over Fading Channels: a Unified
                 Approach to Performance Analysis",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xix + 544",
  year =         "2000",
  ISBN =         "0-471-31779-9",
  ISBN-13 =      "978-0-471-31779-1",
  LCCN =         "TK5103.7 .S523 2000",
  bibdate =      "Sat Dec 16 17:34:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley series in telecommunications and signal
                 processing",
  URL =          "http://www.loc.gov/catdir/bios/wiley043/99056352.html;
                 http://www.loc.gov/catdir/description/wiley035/99056352.html;
                 http://www.loc.gov/catdir/toc/onix06/99056352.html",
  acknowledgement = ack-nhfb,
  author-dates = "1939--",
  subject =      "Digital communications; Reliability; Mathematics;
                 Radio; Transmitters and transmission; Fading",
  tableofcontents = "1.1: System Performance Measures 4 \\
                 1.1.1: Average Signal-to-Noise Ratio 4 \\
                 1.1.2: Outage Probability 5 \\
                 1.1.3: Average Bit Error Probability 6 \\
                 Chapter 2: Fading Channel Characterization and Modeling
                 15 \\
                 2.1: Main Characteristics of Fading Channels 15 \\
                 2.1.1: Envelope and Phase Fluctuations 15 \\
                 2.1.2: Slow and Fast Fading 16 \\
                 2.1.3: Frequency-Flat and Frequency-Selective Fading 16
                 \\
                 2.2: Modeling of Flat Fading Channels 17 \\
                 2.2.1: Multipath Fading 18 \\
                 2.2.2: Log-Normal Shadowing 23 \\
                 2.2.3: Composite Multipath/Shadowing 24 \\
                 2.2.4: Combined (Time-Shared) Shadowed/Unshadowed
                 Fading 25 \\
                 2.3: Modeling of Frequency-Selective Fading Channels 26
                 \\
                 Chapter 3: Types of Communication 31 \\
                 3.1: Ideal Coherent Detection 31 \\
                 3.1.1: Multiple Amplitude-Shift-Keying or Multiple
                 Amplitude Modulation 33 \\
                 3.1.2: Quadrature Amplitude-Shift-Keying or Quadrature
                 Amplitude Modulation 34 \\
                 3.1.3: M-ary Phase-Shift-Keying 35 \\
                 3.1.4: Differentially Encoded M-ary Phase-Shift-Keying
                 39 \\
                 3.1.5: Offset QPSK or Staggered QPSK 41 \\
                 3.1.6: M-ary Frequency-Shift-Keying 43 \\
                 3.1.7: Minimum-Shift-Keying 45 \\
                 3.2: Nonideal Coherent Detection 47 \\
                 3.3: Noncoherent Detection 53 \\
                 3.4: Partially Coherent Detection 55 \\
                 3.4.1: Conventional Detection: One-Symbol Observation
                 55 \\
                 3.4.2: Multiple Symbol Detection 57 \\
                 3.5: Differentially Coherent Detection 59 \\
                 3.5.1: M-ary Differential Phase Shift Keying 59 \\
                 3.5.2: [pi]/4-Differential QPSK 65 \\
                 Part 2: Mathematical Tools \\
                 Chapter 4: Alternative Representations of Classical
                 Functions 69 \\
                 4.1: Gaussian $Q$-Function 70 \\
                 4.1.1: One-Dimensional Case 70 \\
                 4.1.2: Two-Dimensional Case 72 \\
                 4.2: Marcum $Q$-Function 74 \\
                 4.2.1: First-Order Marcum $Q$-Function 74 \\
                 4.2.2: Generalized ($m$th-Order) Marcum $Q$-Function 81
                 \\
                 4.3: Other Functions 90 \\
                 Appendix 4A: Derivation of Eq. (4.2) 95 \\
                 Chapter 5: Useful Expressions for Evaluating Average
                 Error Probability Performance 99 \\
                 5.1: Integrals Involving the Gaussian $Q$-Function 99
                 \\
                 5.1.1: Rayleigh Fading Channel 101 \\
                 5.1.2: Nakagami-q (Hoyt) Fading Channel 101 \\
                 5.1.3: Nakagami-n (Rice) Fading Channel 102 \\
                 5.1.4: Nakagami-m Fading Channel 102 \\
                 5.1.5: Log-Normal Shadowing Channel 104 \\
                 5.1.6: Composite Log-Normal Shadowing/Nakagami-m Fading
                 Channel 104 \\
                 5.2: Integrals Involving the Marcum $Q$-Function 107
                 \\
                 5.2.1: Rayleigh Fading Channel 108 \\
                 5.2.2: Nakagami-q (Hoyt) Fading Channel 109 \\
                 5.2.3: Nakagami-n (Rice) Fading Channel 109 \\
                 5.2.4: Nakagami-m Fading Channel 109 \\
                 5.2.5: Log-Normal Shadowing Channel 109 \\
                 5.2.6: Composite Log-Normal Shadowing/Nakagami-m Fading
                 Channel 110 \\
                 5.3: Integrals Involving the Incomplete Gamma Function
                 111 \\
                 5.3.1: Rayleigh Fading Channel 112 \\
                 5.3.2: Nakagami-q (Hoyt) Fading Channel 112 \\
                 5.3.3: Nakagami-n (Rice) Fading Channel 112 \\
                 5.3.4: Nakagami-m Fading Channel 113 \\
                 5.3.5: Log-Normal Shadowing Channel 114 \\
                 5.3.6: Composite Log-Normal Shadowing/Nakagami-m Fading
                 Channel 114 \\
                 5.4: Integrals Involving Other Functions 114 \\
                 5.4.1: M-PSK Error Probability Integral 114 \\
                 5.4.2: Arbitrary Two-Dimensional Signal Constellation
                 Error Probability Integral 116 \\
                 5.4.3: Integer Powers of the Gaussian $Q$-Function 117
                 \\
                 5.4.4: Integer Powers of M-PSK Error Probability
                 Integrals 121 \\
                 Appendix 5A: Evaluation of Definite Integrals
                 Associated with Rayleigh and Nakagami-$m$ Fading 124
                 \\
                 Chapter 6: New Representations of Some PDF's and CDF's
                 for Correlative Fading Applications 141 \\
                 6.1: Bivariate Rayleigh PDF and CDF 142 \\
                 6.2: PDF and CDF for Maximum of Two Rayleigh Random
                 Variables 146 \\
                 6.3: PDF and CDF for Maximum of Two Nakagami-m Random
                 Variables 149 \\
                 Part 3: Optimum Reception and Performance Evaluation
                 \\
                 Chapter 7: Optimum Receivers for Fading Channels 157
                 \\
                 7.1: Case of Known Amplitudes, Phases, and Delays:
                 Coherent, Detection 159 \\
                 7.2: Case of Known Phases and Delays, Unknown
                 Amplitudes 163 \\
                 7.2.1: Rayleigh Fading 163 \\
                 7.2.2: Nakagami-m Fading 164 \\
                 7.3: Case of Known Amplitudes and Delays, Unknown
                 Phases 166 \\
                 7.4: Case of Known Delays and Unknown Amplitudes and
                 Phases 168 \\
                 7.4.1: One-Symbol Observation: Noncoherent Detection
                 168 \\
                 7.4.2: Two-Symbol Observation: Conventional
                 Differentially Coherent Detection 181 \\
                 7.4.3: N-Symbol Observation: Multiple Symbol
                 Differentially Coherent Detection 186 \\
                 7.5: Case of Unknown Amplitudes, Phases, and Delays 188
                 \\
                 7.5.1: One-Symbol Observation: Noncoherent Detection
                 188 \\
                 7.5.2: Two-Symbol Observation: Conventional
                 Differentially Coherent Detection 190 \\
                 Chapter 8: Performance of Single Channel Receives 193
                 \\
                 8.1: Performance Over the AWGN Channel 193 \\
                 8.1.1: Ideal Coherent Detection 194 \\
                 8.1.2: Nonideal Coherent Detection 206 \\
                 8.1.3: Noncoherent Detection 209 \\
                 8.1.4: Partially Coherent Detection 210 \\
                 8.1.5: Differentially Coherent Detection 213 \\
                 8.1.6: Generic Results for Binary Signaling 218 \\
                 8.2: Performance Over Fading Channels 219 \\
                 8.2.1: Ideal Coherent Detection 220 \\
                 8.2.2: Nonideal Coherent Detection 234 \\
                 8.2.3: Noncoherent Detection 239 \\
                 8.2.4: Partially Coherent Detection 242 \\
                 8.2.5: Differentially Coherent Detection 243 \\
                 Appendix 8A: Stein's Unified Analysis of the Error
                 Probability Performance of Certain Communication
                 Systems 253 \\
                 Chapter 9: Performance of Multichannel Receivers 259
                 \\
                 9.1: Diversity Combining 260 \\
                 9.1.1: Diversity Concept 260 \\
                 9.1.2: Mathematical Modeling 260 \\
                 9.1.3: Brief Survey of Diversity Combining Techniques
                 261 \\
                 9.1.4: Complexity-Performance Trade-offs 264 \\
                 9.2: Maximal-Ratio Combining 265 \\
                 9.2.1: Receiver Structure 265 \\
                 9.2.2: PDF-Based Approach 267 \\
                 9.2.3: MGF-Based Approach 268 \\
                 9.2.4: Bounds and Asymptotic SER Expressions 275 \\
                 9.3: Coherent Equal Gain Combining 278 \\
                 9.3.1: Receiver Structure 279 \\
                 9.3.2: Average Output SNR 279 \\
                 9.3.3: Exact Error Rate Analysis 281 \\
                 9.3.4: Approximate Error Rate Analysis 288 \\
                 9.3.5: Asymptotic Error Rate Analysis 289 \\
                 9.4: Noncoherent Equal-Gain Combining 290 \\
                 9.4.1: DPSK, DQPSK, and BFSK: Exact and Bounds 290 \\
                 9.4.2: M-ary Orthogonal FSK 304 \\
                 9.5: Outage Probability Performance 311 \\
                 9.5.1: MRC and Noncoherent EGC 312 \\
                 9.5.2: Coherent EGC 313 \\
                 9.5.3: Numerical Examples 314 \\
                 9.6: Impact of Fading Correlation 316 \\
                 9.6.1: Model A: Two Correlated Branches with
                 Nonidentical Fading 320 \\
                 9.6.2: Model B: D Identically Distributed Branches with
                 Constant Correlation 323 \\
                 9.6.3: Model C: D Identically Distributed Branches with
                 Exponential Correlation 324 \\
                 9.6.4: Model D: D Nonidentically Distributed Branches
                 with Arbitrary Correlation 325 \\
                 9.6.5: Numerical Examples 329 \\
                 9.7: Selection Combining 333 \\
                 9.7.1: MGF of Output SNR 335 \\
                 9.7.2: Average Output SNR 336 \\
                 9.7.3: Outage Probability 338 \\
                 9.7.4: Average Probability of Error 340 \\
                 9.8: Switched Diversity 348 \\
                 9.8.1: Performance of SSC over Independent Identically
                 Distributed Branches 348 \\
                 9.8.2: Effect of Branch Unbalance 362 \\
                 9.8.3: Effect of Branch Correlation 366 \\
                 9.9: Performance in the Presence of Outdated or
                 Imperfect Channel Estimates 370 \\
                 9.9.1: Maximal-Ratio Combining 370 \\
                 9.9.2: Noncoherent EGC over Rician Fast Fading 371 \\
                 9.9.3: Selection Combining 373 \\
                 9.9.4: Switched Diversity 374 \\
                 9.9.5: Numerical Results 377 \\
                 9.10: Hybrid Diversity Schemes 378 \\
                 9.10.1: Generalized Selection Combining 378 \\
                 9.10.2: Generalized Switched Diversity 403 \\
                 9.10.3: Two-Dimensional Diversity Schemes 408 \\
                 Appendix 9A: Alternative Forms of the Bit Error
                 Probability for a Decision Statistic that is a
                 Quadratic Form of Complex Gaussian Random Variables 421
                 \\
                 Appendix 9B: Simple Numerical Techniques for thee
                 Inversion of the Laplace Transform of Cumulative
                 Distribution Functions 427 \\
                 9B.1: Euler Summation-Based Technique 427 \\
                 9B.2: Gauss-Chebyshev Quadrature-Based Technique 428
                 \\
                 Appendix 9C: Proof of Theorem 1 430 \\
                 Appendix 9D: Direct Proof of Eq. (9.331) 431 \\
                 Appendix 9E: Special Definite Integrals 432 \\
                 Part 4: Application in Practical Communication Systems
                 \\
                 Chapter 10: Optimum Combining: A Diversity Technique
                 for Communication Over Fading Channels in the Presence
                 of Interference 437 \\
                 10.1: Performance of Optimum Combining Receivers 438
                 \\
                 10.1.1: Single Interferer, Independent Identically
                 Distributed Fading 438 \\
                 10.1.2: Multiple Interferers, Independent Identically
                 Distributed Fading 454 \\
                 10.1.3: Comparison with Results for MRC in the Presence
                 of Interference 466 \\
                 Chapter 11: Direct-Sequence Code-Division Multiple
                 Access 473 \\
                 11.1: Single-Carrier DS-CDMA Systems 474 \\
                 11.1.1: System and Channel Models 474 \\
                 11.1.2: Performance Analysis 477 \\
                 11.2: Multicarrier DS-CDMA Systems 479 \\
                 11.2.1: System and Channel Models 480 \\
                 11.2.2: Performance Analysis 483 \\
                 11.2.3: Numerical Examples 489 \\
                 Part 5: Further Extensions \\
                 Chapter 12: Coded Communication Over Fading Channels
                 497 \\
                 12.1: Coherent Detection 499 \\
                 12.1.1: System Model 499 \\
                 12.1.2: Evaluation of Pairwise Error Probability 502
                 \\
                 12.1.3: Transfer Function Bound on Average Bit Error
                 Probability 510 \\
                 12.1.4: Alternative Formulation of the Transfer
                 Function Bound 513 \\
                 12.2: Differentially Coherent Detection 520 \\
                 12.2.1: System Model 520 \\
                 12.2.2: Performance Evaluation 522 \\
                 12.3: Numerical Results: Comparison of the True Upper
                 Bounds and Union-Chernoff Bounds 526 \\
                 Appendix 12A: Evaluation of a Moment Generating
                 Function Associated with Differential Detection of
                 M-PSK Sequences 532",
}


