# bibtab

bibtype: article
filename: elefunt.bib
label: Plagianakos:2001:LCP
author: V. P. Plagianakos and N. K. Nousis and M. N. Vrahatis
title: Locating and computing in parallel all the simple roots of special functions using PVM
journal: j-J-COMPUT-APPL-MATH
volume: 133
number: 1--2
pages: 545--554
day: 1
month: aug
monthnumber: 8
year: 2001
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(00)00675-0
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:19 MST 2017
bibtimestamp: 2017.02.25 12:45:19 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700006750
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: V. P. Plagianakos and N. K. Nousis and M. N. Vrahatis
rawtitle: Locating and computing in parallel all the simple roots of special functions using {PVM}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib; https://www.math.utah.edu/pub/tex/bib/pvm.bib

entry:
@Article{Plagianakos:2001:LCP,
  author =       "V. P. Plagianakos and N. K. Nousis and M. N.
                 Vrahatis",
  title =        "Locating and computing in parallel all the simple
                 roots of special functions using {PVM}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "545--554",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00675-0",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700006750",
  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: Plofker:2001:EIT
author: Kim Plofker
title: The ``Error'' in the Indian ``Taylor Series Approximation'' to the Sine
journal: j-HIST-MATH
volume: 28
number: 4
pages: 283--295
month: nov
monthnumber: 11
year: 2001
CODEN: HIMADS
DOI: https://doi.org/10.1006/hmat.2001.2331
ISSN: 0315-0860 (print), 1090-249X (electronic) OR 03150860 (print), 1090249X (electronic)
ISSNL: 0315-0860 OR 03150860
bibdate: Wed Jun 26 06:20:02 MDT 2013
bibtimestamp: 2013.06.26 06:20:02 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0315086001923316
fjournal: Historia Mathematica
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03150860
rawauthor: Kim Plofker
rawtitle: The {``Error''} in the {Indian} ``{Taylor} Series Approximation'' to the Sine
entry:
@Article{Plofker:2001:EIT,
  author =       "Kim Plofker",
  title =        "The {``Error''} in the {Indian} ``{Taylor} Series
                 Approximation'' to the Sine",
  journal =      j-HIST-MATH,
  volume =       "28",
  number =       "4",
  pages =        "283--295",
  month =        nov,
  year =         "2001",
  CODEN =        "HIMADS",
  DOI =          "https://doi.org/10.1006/hmat.2001.2331",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:20:02 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/S0315086001923316",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}


bibtype: article
filename: elefunt.bib
label: Rabi:2001:OCA
author: J. A. Rabi and M. J. S. de Lemos
journal: j-APPL-MATH-COMP
volume: 124
number: 2
pages: 215--226
day: 25
month: oct
monthnumber: 10
year: 2001
CODEN: AMHCBQ
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Sun Nov 18 09:58:00 MST 2001
bibsource: http://www.elsevier.com/locate/issn/00963003; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2001.11.18 09:58:00 MST
URL: http://www.elsevier.com/gej-ng/10/9/12/113/31/31/abstract.html
fjournal: Applied Mathematics and Computation
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: J. A. Rabi and M. J. S. de Lemos
title:
Optimization of convergence acceleration in multigrid numerical solutions of conductive-convective problems

rawtitle:
Optimization of convergence acceleration in multigrid numerical solutions of conductive-convective problems

entry:
@Article{Rabi:2001:OCA,
  author =       "J. A. Rabi and M. J. S. de Lemos",
  title =        "Optimization of convergence acceleration in multigrid
                 numerical solutions of conductive-convective problems",
  journal =      j-APPL-MATH-COMP,
  volume =       "124",
  number =       "2",
  pages =        "215--226",
  day =          "25",
  month =        oct,
  year =         "2001",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sun Nov 18 09:58:00 MST 2001",
  bibsource =    "http://www.elsevier.com/locate/issn/00963003;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/gej-ng/10/9/12/113/31/31/abstract.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Rahavachary:2001:LSS
author: Saty Rahavachary
title: Letters: Setting the tt sqrt() record straight
journal: j-DDJ
volume: 26
number: 4
pages: 12--12
month: apr
monthnumber: 4
year: 2001
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Tue Mar 13 15:22:36 MST 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2001.03.13 15:22:36 MST
URL: http://www.ddj.com/
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Saty Rahavachary
rawtitle: Letters: Setting the {\tt sqrt()} record straight
entry:
@Article{Rahavachary:2001:LSS,
  author =       "Saty Rahavachary",
  title =        "Letters: Setting the {\tt sqrt()} record straight",
  journal =      j-DDJ,
  volume =       "26",
  number =       "4",
  pages =        "12--12",
  month =        apr,
  year =         "2001",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Mar 13 15:22:36 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ddj.com/",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: elefunt.bib
label: Rappoport:2001:CVP
author: J. M. Rappoport
journal: j-COMPUT-MATH-APPL
volume: 41
number: 3--4
pages: 399--406
month: feb
monthnumber: 2
year: 2001
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:49:14 MST 2017
bibtimestamp: 2017.03.01 21:49:14 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122100002820
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: J. M. Rappoport
title:
Canonical vector polynomials for the computation of complex order Bessel functions with the tau method

bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Canonical vector polynomials for the computation of complex order {Bessel} functions with the tau method

entry:
@Article{Rappoport:2001:CVP,
  author =       "J. M. Rappoport",
  title =        "Canonical vector polynomials for the computation of
                 complex order {Bessel} functions with the tau method",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "41",
  number =       "3--4",
  pages =        "399--406",
  month =        feb,
  year =         "2001",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:14 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122100002820",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Rump:2001:RPS
author: Siegfried M. Rump
title: Rigorous and Portable Standard Functions
journal: j-BIT-NUM-MATH
volume: 41
number: 3
pages: 540--562
month: jun
monthnumber: 6
year: 2001
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1023/A:1021971313412
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 15:06:04 MST 2006
bibtimestamp: 2006.01.04 15:06:04 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=540
keywords: elementary functions; floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Siegfried M. Rump
rawtitle: Rigorous and Portable Standard Functions
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3; http://www.mai.liu.se/BIT/contents/bit41.html; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Today's floating point implementations of elementary transcendental functions are usually very accurate. However, with few exceptions, the actual accuracy is not known. In the present paper we describe a rigorous, accurate, fast and portable implementation of the elementary standard functions based on some existing approximate standard functions. The scheme is outlined for IEEE 754, but not difficult to adapt to other floating point formats. A Matlab implementation is available on the net. Accuracy of the proposed algorithms can be rigorously estimated. As an example we prove that the relative accuracy of the exponential function is better than 2.07 eps in a slightly reduced argument range (eps denoting the relative rounding error unit). Otherwise, extensive computational tests suggest for all elementary functions and all suitable arguments an accuracy better than about 3 eps.

rawabstract:
Today's floating point implementations of elementary transcendental functions are usually very accurate. However, with few exceptions, the actual accuracy is not known. In the present paper we describe a rigorous, accurate, fast and portable implementation of the elementary standard functions based on some existing approximate standard functions. The scheme is outlined for IEEE 754, but not difficult to adapt to other floating point formats. A Matlab implementation is available on the net. Accuracy of the proposed algorithms can be rigorously estimated. As an example we prove that the relative accuracy of the exponential function is better than 2.07 eps in a slightly reduced argument range (eps denoting the relative rounding error unit). Otherwise, extensive computational tests suggest for all elementary functions and all suitable arguments an accuracy better than about 3 eps.

entry:
@Article{Rump:2001:RPS,
  author =       "Siegfried M. Rump",
  title =        "Rigorous and Portable Standard Functions",
  journal =      j-BIT-NUM-MATH,
  volume =       "41",
  number =       "3",
  pages =        "540--562",
  month =        jun,
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1023/A:1021971313412",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 15:06:04 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
                 http://www.mai.liu.se/BIT/contents/bit41.html;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=540",
  abstract =     "Today's floating point implementations of elementary
                 transcendental functions are usually very accurate.
                 However, with few exceptions, the actual accuracy is
                 not known. In the present paper we describe a rigorous,
                 accurate, fast and portable implementation of the
                 elementary standard functions based on some existing
                 approximate standard functions. The scheme is outlined
                 for IEEE 754, but not difficult to adapt to other
                 floating point formats. A Matlab implementation is
                 available on the net. Accuracy of the proposed
                 algorithms can be rigorously estimated. As an example
                 we prove that the relative accuracy of the exponential
                 function is better than 2.07 eps in a slightly reduced
                 argument range (eps denoting the relative rounding
                 error unit). Otherwise, extensive computational tests
                 suggest for all elementary functions and all suitable
                 arguments an accuracy better than about 3 eps.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elementary functions; floating-point arithmetic",
}


bibtype: article
filename: elefunt.bib
label: Smith:2001:AFS
author: David M. Smith
journal: j-TOMS
volume: 27
number: 4
pages: 377--387
month: dec
monthnumber: 12
year: 2001
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Mar 13 08:49:29 MST 2002
bibtimestamp: 2002.03.13 08:49:29 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: David M. Smith
title:
Algorithm 814: Fortran 90 software for floating-point multiple precision arithmetic, gamma and related functions

rawtitle:
{Algorithm 814}: {Fortran 90} software for floating-point multiple precision arithmetic, gamma and related functions

entry:
@Article{Smith:2001:AFS,
  author =       "David M. Smith",
  title =        "{Algorithm 814}: {Fortran 90} software for
                 floating-point multiple precision arithmetic, gamma and
                 related functions",
  journal =      j-TOMS,
  volume =       "27",
  number =       "4",
  pages =        "377--387",
  month =        dec,
  year =         "2001",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 13 08:49:29 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",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: book
filename: elefunt.bib
label: Srivastava:2001:SAZ
author: H. M. Srivastava and Choi Junesang
title: Series Associated with the Zeta and Related Functions
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: ix + 388
year: 2001
DOI: https://doi.org/10.1007/978-94-015-9672-5
ISBN: 0-7923-7054-6 OR 0792370546
ISBN13: 978-0-7923-7054-3 OR 9780792370543
LCCN: QA351 .S74 2001
bibdate: Wed Jun 10 16:22:26 MDT 2015
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2015.06.10 16:22:26 MDT
subject: Functions, Zeta; Series
acknowledgement: ack-nhfb
rawauthor: H. M. Srivastava and Choi Junesang
rawtitle: Series Associated with the Zeta and Related Functions
URL:
http://www.loc.gov/catdir/enhancements/fy0822/2001035764-d.html; http://www.loc.gov/catdir/enhancements/fy0822/2001035764-t.html

TOC:
Acknowledgements / ix 1. Introduction and Preliminaries 1.1. Gamma and Beta functions / 1 1.2. Polygamma functions / 13 1.3. The multiple Gamma functions / 24 1.4. The Gaussian hypergeometric function and its generalization / 44 1.5. Stirling numbers of the first and second kind / 56 1.6. Bernoulli and Euler polynomials and numbers / 59 Problems / 67 2. The Zeta and Related Functions 2.1. Multiple Hurwitz Zeta functions / 77 2.2. The Hurwitz (or generalized) Zeta function / 88 2.3. The Riemann Zeta function / 96 2.4. Polylogarithm functions / 106 2.5. Hurwitz--Lerch Zeta functions / 121 Problems / 128 3. Series Involving Zeta Functions 3.1. Historical introduction / 142 3.2. Use of the Binomial theorem / 143 3.3. Use of generating functions / 152 3.4. Use of multiple Gamma functions / 159 3.5. Use of hypergeometric identities / 250 3.6. Other methods and their applications / 260 Problems / 269 4. Evaluations and Series Representations 4.1. Evaluation of $zeta (2n)$ / 275 4.2. Rapidly convergent series for $zeta (2n + 1)$ / 280 4.3. Further series representations / 289 4.4. Computational results / 295 Problems / 304 5. Determinants of the Laplacians 5.1. The $n$-dimensional problem / 315 5.2. Computations using the simple and multiple Gamma functions / 318 5.3. Computations using series of Zeta functions / 325 5.4. Remarks and observations / 328 Problems / 329 6. Miscellaneous Results 6.1. Bernoulli and Euler polynomials at rational arguments / 335 6.2. Closed-form summation of trigonometric series / 341 6.3. Integrals associated with the use of the Euler--Maclaurin summation formula / 344 Problems / 350 Bibliography / 353 Author Index / 379 Subject Index / 383

rawTOC:
Acknowledgements / ix \\ 1. Introduction and Preliminaries \\ 1.1. Gamma and Beta functions / 1 \\ 1.2. Polygamma functions / 13 \\ 1.3. The multiple Gamma functions / 24 \\ 1.4. The Gaussian hypergeometric function and its generalization / 44 \\ 1.5. Stirling numbers of the first and second kind / 56 \\ 1.6. Bernoulli and Euler polynomials and numbers / 59 \\ Problems / 67 \\ 2. The Zeta and Related Functions \\ 2.1. Multiple Hurwitz Zeta functions / 77 \\ 2.2. The Hurwitz (or generalized) Zeta function / 88 \\ 2.3. The Riemann Zeta function / 96 \\ 2.4. Polylogarithm functions / 106 \\ 2.5. Hurwitz--Lerch Zeta functions / 121 \\ Problems / 128 \\ 3. Series Involving Zeta Functions \\ 3.1. Historical introduction / 142 \\ 3.2. Use of the Binomial theorem / 143 \\ 3.3. Use of generating functions / 152 \\ 3.4. Use of multiple Gamma functions / 159 \\ 3.5. Use of hypergeometric identities / 250 \\ 3.6. Other methods and their applications / 260 \\ Problems / 269 \\ 4. Evaluations and Series Representations \\ 4.1. Evaluation of $\zeta(2n)$ / 275 \\ 4.2. Rapidly convergent series for $\zeta(2n + 1)$ / 280 \\ 4.3. Further series representations / 289 \\ 4.4. Computational results / 295 \\ Problems / 304 \\ 5. Determinants of the Laplacians \\ 5.1. The $n$-dimensional problem / 315 \\ 5.2. Computations using the simple and multiple Gamma functions / 318 \\ 5.3. Computations using series of Zeta functions / 325 \\ 5.4. Remarks and observations / 328 \\ Problems / 329 \\ 6. Miscellaneous Results \\ 6.1. Bernoulli and Euler polynomials at rational arguments / 335 \\ 6.2. Closed-form summation of trigonometric series / 341 \\ 6.3. Integrals associated with the use of the Euler--Maclaurin summation formula / 344 \\ Problems / 350 \\ Bibliography / 353 \\ Author Index / 379 \\ Subject Index / 383

entry:
@Book{Srivastava:2001:SAZ,
  author =       "H. M. Srivastava and Choi Junesang",
  title =        "Series Associated with the Zeta and Related
                 Functions",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "ix + 388",
  year =         "2001",
  DOI =          "https://doi.org/10.1007/978-94-015-9672-5",
  ISBN =         "0-7923-7054-6",
  ISBN-13 =      "978-0-7923-7054-3",
  LCCN =         "QA351 .S74 2001",
  bibdate =      "Wed Jun 10 16:22:26 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0822/2001035764-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0822/2001035764-t.html",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Zeta; Series",
  tableofcontents = "Acknowledgements / ix \\
                 1. Introduction and Preliminaries \\
                 1.1. Gamma and Beta functions / 1 \\
                 1.2. Polygamma functions / 13 \\
                 1.3. The multiple Gamma functions / 24 \\
                 1.4. The Gaussian hypergeometric function and its
                 generalization / 44 \\
                 1.5. Stirling numbers of the first and second kind / 56
                 \\
                 1.6. Bernoulli and Euler polynomials and numbers / 59
                 \\
                 Problems / 67 \\
                 2. The Zeta and Related Functions \\
                 2.1. Multiple Hurwitz Zeta functions / 77 \\
                 2.2. The Hurwitz (or generalized) Zeta function / 88
                 \\
                 2.3. The Riemann Zeta function / 96 \\
                 2.4. Polylogarithm functions / 106 \\
                 2.5. Hurwitz--Lerch Zeta functions / 121 \\
                 Problems / 128 \\
                 3. Series Involving Zeta Functions \\
                 3.1. Historical introduction / 142 \\
                 3.2. Use of the Binomial theorem / 143 \\
                 3.3. Use of generating functions / 152 \\
                 3.4. Use of multiple Gamma functions / 159 \\
                 3.5. Use of hypergeometric identities / 250 \\
                 3.6. Other methods and their applications / 260 \\
                 Problems / 269 \\
                 4. Evaluations and Series Representations \\
                 4.1. Evaluation of $\zeta(2n)$ / 275 \\
                 4.2. Rapidly convergent series for $\zeta(2n + 1)$ /
                 280 \\
                 4.3. Further series representations / 289 \\
                 4.4. Computational results / 295 \\
                 Problems / 304 \\
                 5. Determinants of the Laplacians \\
                 5.1. The $n$-dimensional problem / 315 \\
                 5.2. Computations using the simple and multiple Gamma
                 functions / 318 \\
                 5.3. Computations using series of Zeta functions / 325
                 \\
                 5.4. Remarks and observations / 328 \\
                 Problems / 329 \\
                 6. Miscellaneous Results \\
                 6.1. Bernoulli and Euler polynomials at rational
                 arguments / 335 \\
                 6.2. Closed-form summation of trigonometric series /
                 341 \\
                 6.3. Integrals associated with the use of the
                 Euler--Maclaurin summation formula / 344 \\
                 Problems / 350 \\
                 Bibliography / 353 \\
                 Author Index / 379 \\
                 Subject Index / 383",
}


bibtype: inproceedings
filename: elefunt.bib
label: Takagi:2001:HAC
author: N. Takagi
booktitle: Proceedings of the 15th IEEE Symposium on Computer Arithmetic, 11--13 June 2001
title: A Hardware Algorithm for Computing Reciprocal Square Root
crossref: Burgess:2001:ISC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 94--100
year: 2001
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: N. Takagi
rawbooktitle: Proceedings of the 15th {IEEE} Symposium on Computer Arithmetic, 11--13 June 2001
rawtitle: A Hardware Algorithm for Computing Reciprocal Square Root
entry:
@InProceedings{Takagi:2001:HAC,
  author =       "N. Takagi",
  booktitle =    "Proceedings of the 15th {IEEE} Symposium on Computer
                 Arithmetic, 11--13 June 2001",
  title =        "A Hardware Algorithm for Computing Reciprocal Square
                 Root",
  crossref =     "Burgess:2001:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "94--100",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "A hardware algorithm for computing the reciprocal
                 square root which appears frequently in multimedia and
                 graphics applications is proposed. The reciprocal
                 square root is computed by iteration of
                 carry-propagation-free additions, shifts, and
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Thorsley:2001:AEH
author: Michael D. Thorsley and Marita C. Chidichimo
title: An asymptotic expansion for the hypergeometric function $_2 F_1 (a, b; c; x)$
journal: j-J-MATH-PHYS
volume: 42
number: 4
pages: 1921--1930
month: apr
monthnumber: 4
year: 2001
CODEN: JMAPAQ
ISSNL: 0022-2488 OR 00222488
bibdate: Wed Apr 18 05:33:53 MDT 2001
bibtimestamp: 2001.04.18 05:33:53 MDT
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: Michael D. Thorsley and Marita C. Chidichimo
rawtitle: An asymptotic expansion for the hypergeometric function {$_2 F_1 (a, b; c; x)$}
bibsource:
http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib

entry:
@Article{Thorsley:2001:AEH,
  author =       "Michael D. Thorsley and Marita C. Chidichimo",
  title =        "An asymptotic expansion for the hypergeometric
                 function {$_2 F_1 (a, b; c; x)$}",
  journal =      j-J-MATH-PHYS,
  volume =       "42",
  number =       "4",
  pages =        "1921--1930",
  month =        apr,
  year =         "2001",
  CODEN =        "JMAPAQ",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Wed Apr 18 05:33:53 MDT 2001",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
}


bibtype: article
filename: elefunt.bib
label: Verdonk:2001:PRIa
author: Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren
journal: j-TOMS
volume: 27
number: 1
pages: 92--118
month: mar
monthnumber: 3
year: 2001
CODEN: ACMSCU
DOI: https://doi.org/10.1145/382043.382404
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
URL: http://doi.acm.org/10.1145/382043.382404; http://www.win.ua.ac.be/~cant/ieeecc754.html
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren
title:
A precision- and range-independent tool for testing floating-point arithmetic I: Basic operations, square root, and remainder

bibsource:
http://www.acm.org/pubs/contents/journals/toms/; 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/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
This paper introduces a precision- and range-independent tool for testing the compliance of hardware or software implementations of (multiprecision) floating-point arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, offering many options to test only specific aspects of the IEEE standards, and a large set of test vectors, encoded in a precision-independent syntax to allow the testing of basic and extended hardware formats as well as multiprecision floating-point implementations. The suite of test vectors stems on one hand from the integration and fully precision- and range-independent generalization of existing hardware test sets, and on the other hand from the systematic testing of exact rounding for all combinations of round and sticky bits that can occur. The former constitutes only 50% of the resulting test set. In the latter we especially focus on hard-to-round cases. In addition, the test suite implicitly tests properties of floating-point operations, following the idea of Paranoia, and it reports which of the three IEEE-compliant underflow mechanisms is used by the floating-point implementation under consideration. We also check whether that underflow mechanism is used consistently. The tool is backward compatible with the UCBTEST package and with Coonen's test syntax.

keywords:
arithmetic; floating-point; floating-point testing; IEEE floating-point standard; multiprecision; validation; Verification

subject:
Primary Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer arithmetic Additional Classification: D. Software D.3 PROGRAMMING LANGUAGES D.3.0 General Subjects: Standards

rawabstract:
This paper introduces a precision- and range-independent tool for testing the compliance of hardware or software implementations of (multiprecision) floating-point arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, offering many options to test only specific aspects of the IEEE standards, and a large set of test vectors, encoded in a precision-independent syntax to allow the testing of basic and extended hardware formats as well as multiprecision floating-point implementations. The suite of test vectors stems on one hand from the integration and fully precision- and range-independent generalization of existing hardware test sets, and on the other hand from the systematic testing of exact rounding for all combinations of round and sticky bits that can occur. The former constitutes only 50\% of the resulting test set. In the latter we especially focus on hard-to-round cases. In addition, the test suite implicitly tests properties of floating-point operations, following the idea of Paranoia, and it reports which of the three IEEE-compliant underflow mechanisms is used by the floating-point implementation under consideration. We also check whether that underflow mechanism is used consistently. The tool is backward compatible with the UCBTEST package and with Coonen's test syntax.

rawtitle:
A precision- and range-independent tool for testing floating-point arithmetic {I}: {Basic} operations, square root, and remainder

entry:
@Article{Verdonk:2001:PRIa,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A precision- and range-independent tool for testing
                 floating-point arithmetic {I}: {Basic} operations,
                 square root, and remainder",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "92--118",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382404",
  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/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/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/382043.382404;
                 http://www.win.ua.ac.be/~cant/ieeecc754.html",
  abstract =     "This paper introduces a precision- and
                 range-independent tool for testing the compliance of
                 hardware or software implementations of
                 (multiprecision) floating-point arithmetic with the
                 principles of the IEEE standards 754 and 854. The tool
                 consists of a driver program, offering many options to
                 test only specific aspects of the IEEE standards, and a
                 large set of test vectors, encoded in a
                 precision-independent syntax to allow the testing of
                 basic and extended hardware formats as well as
                 multiprecision floating-point implementations. The
                 suite of test vectors stems on one hand from the
                 integration and fully precision- and range-independent
                 generalization of existing hardware test sets, and on
                 the other hand from the systematic testing of exact
                 rounding for all combinations of round and sticky bits
                 that can occur. The former constitutes only 50\% of the
                 resulting test set. In the latter we especially focus
                 on hard-to-round cases. In addition, the test suite
                 implicitly tests properties of floating-point
                 operations, following the idea of Paranoia, and it
                 reports which of the three IEEE-compliant underflow
                 mechanisms is used by the floating-point implementation
                 under consideration. We also check whether that
                 underflow mechanism is used consistently. The tool is
                 backward compatible with the UCBTEST package and with
                 Coonen's test syntax.",
  accepted =     "23 February 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "arithmetic; floating-point; floating-point testing;
                 IEEE floating-point standard; multiprecision;
                 validation; Verification",
  subject =      "Primary Classification: G. Mathematics of Computing
                 G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer
                 arithmetic\\
                 Additional Classification: D. Software D.3 PROGRAMMING
                 LANGUAGES D.3.0 General Subjects: Standards",
}


bibtype: article
filename: elefunt.bib
label: Weniger:2001:IID
author: Ernst Joachim Weniger
journal: j-COMP-PHYS-COMM
volume: 133
number: 2--3
pages: 202--228
day: 15
month: jan
monthnumber: 1
year: 2001
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(00)00175-2
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Thu Dec 01 09:12:48 2011
bibtimestamp: 2011.12.01 09:12:48 ???
fjournal: Computer Physics Communications
keywords: convergence acceleration
remark: This paper concentrates on $_2 F_1 (a, b; c; z)$.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Ernst Joachim Weniger
title:
Irregular input data in convergence acceleration and summation processes: General considerations and some special Gaussian hypergeometric series as model problems

bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Irregular input data in convergence acceleration and summation processes: {General} considerations and some special {Gaussian} hypergeometric series as model problems

entry:
@Article{Weniger:2001:IID,
  author =       "Ernst Joachim Weniger",
  title =        "Irregular input data in convergence acceleration and
                 summation processes: {General} considerations and some
                 special {Gaussian} hypergeometric series as model
                 problems",
  journal =      j-COMP-PHYS-COMM,
  volume =       "133",
  number =       "2--3",
  pages =        "202--228",
  day =          "15",
  month =        jan,
  year =         "2001",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(00)00175-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Dec 01 09:12:48 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "convergence acceleration",
  remark =       "This paper concentrates on $_2 F_1 (a, b; c; z)$.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Zheng:2001:ARE
author: Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui
booktitle: Proceedings of the 4th International Conference on ASIC
title: The application of redundant encoding in iterative implementation of division and square root
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 603--606
year: 2001
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: Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui
rawbooktitle: Proceedings of the 4th International Conference on {ASIC}
rawtitle: The application of redundant encoding in iterative implementation of division and square root
entry:
@InProceedings{Zheng:2001:ARE,
  author =       "Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui",
  booktitle =    "Proceedings of the 4th International Conference on
                 {ASIC}",
  title =        "The application of redundant encoding in iterative
                 implementation of division and square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "603--606",
  year =         "2001",
  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 paper is to discuss the speed
                 improvement in division and square root computation
                 with small area penalty. The digit recurrence SRT
                 algorithm and functional iteration Newton--Raphson
                 algorithm are generally used in modern \ldots{}",
}


bibtype: misc
filename: elefunt.bib
label: Ziv:2001:APM
author: Abraham Ziv and Moshe Olshansky and Ealan Henis and Anna Reitman
title: Accurate Portable Mathematical Library (IBM APMathLib)
publisher: pub-IBM
address: pub-IBM:adr
pages: 603--606
day: 20
month: dec
monthnumber: 12
year: 2001
bibdate: Wed Nov 24 08:06:54 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.11.24 08:06:54 ???
URL: ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz; http://oss.software.ibm.com/mathlib/
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: Abraham Ziv and Moshe Olshansky and Ealan Henis and Anna Reitman
rawtitle: Accurate Portable Mathematical Library ({IBM APMathLib})
entry:
@Misc{Ziv:2001:APM,
  author =       "Abraham Ziv and Moshe Olshansky and Ealan Henis and
                 Anna Reitman",
  title =        "Accurate Portable Mathematical Library ({IBM
                 APMathLib})",
  howpublished = "World-Wide Web document",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  day =          "20",
  month =        dec,
  year =         "2001",
  bibdate =      "Wed Nov 24 08:06:54 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz;
                 http://oss.software.ibm.com/mathlib/",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Al-Jarrah:2002:GSB
author: A. Al-Jarrah and K. M. Dempsey and M. L. Glasser
title: Generalized series of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 143
number: 1
pages: 1--8
day: 1
month: jun
monthnumber: 6
year: 2002
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:28 MST 2017
bibtimestamp: 2017.02.25 12:52:28 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042701005052
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: A. Al-Jarrah and K. M. Dempsey and M. L. Glasser
rawtitle: Generalized series of {Bessel} functions
entry:
@Article{Al-Jarrah:2002:GSB,
  author =       "A. Al-Jarrah and K. M. Dempsey and M. L. Glasser",
  title =        "Generalized series of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "143",
  number =       "1",
  pages =        "1--8",
  day =          "1",
  month =        jun,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:28 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/S0377042701005052",
  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: Bertot:2002:PGS
author: Yves Bertot and Nicolas Magaud and Paul Zimmermann
title: A Proof of GMP Square Root
journal: j-J-AUTOM-REASON
volume: 29
number: 3--4
pages: 225--252
month: sep
monthnumber: 9
year: 2002
CODEN: JAREEW
DOI: https://doi.org/10.1023/A:1021987403425
ISSN: 0168-7433 (print), 1573-0670 (electronic) OR 01687433 (print), 15730670 (electronic)
ISSNL: 0168-7433 OR 01687433
bibdate: Sat Feb 08 08:59:09 2020
bibtimestamp: 2020.02.08 08:59:09 ???
URL: https://link.springer.com/article/10.1023/A:1021987403425
fjournal: Journal of Automated Reasoning
keywords: GNU Multiple Precision library
acknowledgement: ack-nhfb
ajournal: J. Autom. Reason.
journalURL: http://link.springer.com/journal/10817
rawauthor: Yves Bertot and Nicolas Magaud and Paul Zimmermann
rawtitle: A Proof of {GMP} Square Root
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/gnu.bib; https://www.math.utah.edu/pub/tex/bib/jautomreason.bib

entry:
@Article{Bertot:2002:PGS,
  author =       "Yves Bertot and Nicolas Magaud and Paul Zimmermann",
  title =        "A Proof of {GMP} Square Root",
  journal =      j-J-AUTOM-REASON,
  volume =       "29",
  number =       "3--4",
  pages =        "225--252",
  month =        sep,
  year =         "2002",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1023/A:1021987403425",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Sat Feb 08 08:59:09 2020",
  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/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "https://link.springer.com/article/10.1023/A:1021987403425",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
  keywords =     "GNU Multiple Precision library",
}


bibtype: incollection
filename: elefunt.bib
label: Boisvert:2002:HMF
author: Ronald F. Boisvert and Daniel W. Lozier
title: Handbook of Mathematical Functions
crossref: Lide:2002:CEM
pages: 135--139
year: 2002
bibdate: Fri Jul 09 06:28:13 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:28:13 ???
note: Also printed as NIST Special Publication 958, Jan. 2001.
acknowledgement: ack-nhfb
rawauthor: Ronald F. Boisvert and Daniel W. Lozier
rawnote: Also printed as NIST Special Publication 958, Jan. 2001.
rawtitle: Handbook of Mathematical Functions
URL:
https://nvlpubs.nist.gov/nistpubs/sp958-lide/135-139.pdf; https://nvlpubs.nist.gov/nistpubs/sp958-lide/html/135-139.html

remark:
This article describes the history of the creation of the famous 1964 book by Milton Abramowitz and Irene Stegun named in the title.

entry:
@InCollection{Boisvert:2002:HMF,
  author =       "Ronald F. Boisvert and Daniel W. Lozier",
  title =        "Handbook of Mathematical Functions",
  crossref =     "Lide:2002:CEM",
  pages =        "135--139",
  year =         "2002",
  bibdate =      "Fri Jul 09 06:28:13 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Also printed as NIST Special Publication 958, Jan.
                 2001.",
  URL =          "https://nvlpubs.nist.gov/nistpubs/sp958-lide/135-139.pdf;
                 https://nvlpubs.nist.gov/nistpubs/sp958-lide/html/135-139.html",
  acknowledgement = ack-nhfb,
  remark =       "This article describes the history of the creation of
                 the famous 1964 book by Milton Abramowitz and Irene
                 Stegun named in the title.",
}


bibtype: article
filename: elefunt.bib
label: Bradford:2002:RAE
title: Reasoning about the elementary functions of complex analysis
journal: j-ANN-MATH-ARTIF-INTELL
volume: 36
number: 3
pages: 303--318
year: 2002
CODEN: AMAIEC
ISSN: 1012-2443 (print), 1573-7470 (electronic) OR 10122443 (print), 15737470 (electronic)
ISSNL: 1012-2443 OR 10122443
MRclass: 30-01 (03B35 68W30)
MRnumber: MR1950025 (2003m:30001)
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 ???
note: Artificial intelligence and symbolic computation (Madrid, 2000)
fjournal: Annals of Mathematics and Artificial Intelligence
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10472
rawnote: Artificial intelligence and symbolic computation (Madrid, 2000)
rawtitle: Reasoning about the elementary functions of complex analysis
author:
Russell Bradford and Robert M. Corless and James H. Davenport and David J. Jeffrey and Stephen M. Watt

rawauthor:
Russell Bradford and Robert M. Corless and James H. Davenport and David J. Jeffrey and Stephen M. Watt

entry:
@Article{Bradford:2002:RAE,
  author =       "Russell Bradford and Robert M. Corless and James H.
                 Davenport and David J. Jeffrey and Stephen M. Watt",
  title =        "Reasoning about the elementary functions of complex
                 analysis",
  journal =      j-ANN-MATH-ARTIF-INTELL,
  volume =       "36",
  number =       "3",
  pages =        "303--318",
  year =         "2002",
  CODEN =        "AMAIEC",
  ISSN =         "1012-2443 (print), 1573-7470 (electronic)",
  ISSN-L =       "1012-2443",
  MRclass =      "30-01 (03B35 68W30)",
  MRnumber =     "MR1950025 (2003m:30001)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Artificial intelligence and symbolic computation
                 (Madrid, 2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematics and Artificial Intelligence",
  journal-URL =  "http://link.springer.com/journal/10472",
}


bibtype: inproceedings
filename: elefunt.bib
label: Bradford:2002:TBS
author: Russell Bradford and James H. Davenport
booktitle: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation
title: Towards better simplification of elementary functions
publisher: pub-ACM
address: pub-ACM:adr
pages: 16--22 (electronic)
year: 2002
MRclass: 68W30 (33B10)
MRnumber: MR2035228
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 ???
acknowledgement: ack-nhfb
rawauthor: Russell Bradford and James H. Davenport
rawbooktitle: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation
rawtitle: Towards better simplification of elementary functions
entry:
@InProceedings{Bradford:2002:TBS,
  author =       "Russell Bradford and James H. Davenport",
  booktitle =    "Proceedings of the 2002 International Symposium on
                 Symbolic and Algebraic Computation",
  title =        "Towards better simplification of elementary
                 functions",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "16--22 (electronic)",
  year =         "2002",
  MRclass =      "68W30 (33B10)",
  MRnumber =     "MR2035228",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Bryc:2002:UAR
author: W. Bryc
title: A uniform approximation to the right normal tail integral
journal: j-APPL-MATH-COMP
volume: 127
number: 2--3
pages: 365--374
day: 15
month: apr
monthnumber: 4
year: 2002
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/S0096-3003(01)00015-7
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Wed Feb 27 08:48:29 MST 2002
bibtimestamp: 2002.02.27 08:48:29 MST
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003/
rawauthor: W. Bryc
rawtitle: A uniform approximation to the right normal tail integral
bibsource:
http://www.elsevier.com/locate/issn/00963003; https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www.elsevier.com/gej-ng/10/9/12/123/27/44/abstract.html; http://www.sciencedirect.com/science/article/pii/S0096300301000157

entry:
@Article{Bryc:2002:UAR,
  author =       "W. Bryc",
  title =        "A uniform approximation to the right normal tail
                 integral",
  journal =      j-APPL-MATH-COMP,
  volume =       "127",
  number =       "2--3",
  pages =        "365--374",
  day =          "15",
  month =        apr,
  year =         "2002",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/S0096-3003(01)00015-7",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Wed Feb 27 08:48:29 MST 2002",
  bibsource =    "http://www.elsevier.com/locate/issn/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/gej-ng/10/9/12/123/27/44/abstract.html;
                 http://www.sciencedirect.com/science/article/pii/S0096300301000157",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}


bibtype: article
filename: elefunt.bib
label: Ceberio:2002:HRI
author: M. Ceberio and L. Granvilliers
title: Horner's Rule for Interval Evaluation Revisited
journal: j-COMPUTING
volume: 69
number: 1
pages: 51--81
month: mar
monthnumber: 3
year: 2002
CODEN: CMPTA2
DOI: https://doi.org/10.1007/s00607-002-1448-y
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Nov 5 07:12:39 MST 2002
bibtimestamp: 2002.11.05 07:12:39 MST
fjournal: Computing
keywords: interval arithmetic; number of multiplications to evaluate a polynomial
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
rawauthor: M. Ceberio and L. Granvilliers
rawtitle: {Horner}'s Rule for Interval Evaluation Revisited
bibsource:
http://link.springer-ny.com/link/service/journals/00607/tocs/t2069001.htm; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://link.springer.de/link/service/journals/00607/bibs/2069001/20690051.htm; http://link.springer.de/link/service/journals/00607/papers/2069001/20690051.pdf

entry:
@Article{Ceberio:2002:HRI,
  author =       "M. Ceberio and L. Granvilliers",
  title =        "{Horner}'s Rule for Interval Evaluation Revisited",
  journal =      j-COMPUTING,
  volume =       "69",
  number =       "1",
  pages =        "51--81",
  month =        mar,
  year =         "2002",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-002-1448-y",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Nov 5 07:12:39 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/journals/00607/tocs/t2069001.htm;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.de/link/service/journals/00607/bibs/2069001/20690051.htm;
                 http://link.springer.de/link/service/journals/00607/papers/2069001/20690051.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "interval arithmetic; number of multiplications to
                 evaluate a polynomial",
}


bibtype: inproceedings
filename: elefunt.bib
label: Chiani:2002:IEB
author: M. Chiani and D. Dardari
booktitle: Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 51--81
year: 2002
DOI: https://doi.org/10.1109/glocom.2002.1188428
bibdate: Sat Dec 16 16:54:47 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 16:54:47 ???
URL: http://ieeexplore.ieee.org/document/1188428/
acknowledgement: ack-nhfb
rawauthor: M. Chiani and D. Dardari
rawbooktitle: Global Telecommunications Conference, 2002. {GLOBECOM '02}. {IEEE}
title:
Improved exponential bounds and approximation for the $Q$-function with application to average error probability computation

rawtitle:
Improved exponential bounds and approximation for the {$Q$}-function with application to average error probability computation

entry:
@InProceedings{Chiani:2002:IEB,
  author =       "M. Chiani and D. Dardari",
  booktitle =    "Global Telecommunications Conference, 2002. {GLOBECOM
                 '02}. {IEEE}",
  title =        "Improved exponential bounds and approximation for the
                 {$Q$}-function with application to average error
                 probability computation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  year =         "2002",
  DOI =          "https://doi.org/10.1109/glocom.2002.1188428",
  bibdate =      "Sat Dec 16 16:54:47 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/1188428/",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Fabijonas:2002:LMC
author: Bruce R. Fabijonas
journal: j-J-COMPUT-APPL-MATH
volume: 146
number: 2
pages: 323--342
day: 15
month: sep
monthnumber: 9
year: 2002
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:30 MST 2017
bibtimestamp: 2017.02.25 12:52:30 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702003643
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Bruce R. Fabijonas
title:
Laplace's method on a computer algebra system with an application to the real valued modified Bessel functions

rawtitle:
{Laplace}'s method on a computer algebra system with an application to the real valued modified {Bessel} functions

entry:
@Article{Fabijonas:2002:LMC,
  author =       "Bruce R. Fabijonas",
  title =        "{Laplace}'s method on a computer algebra system with
                 an application to the real valued modified {Bessel}
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "146",
  number =       "2",
  pages =        "323--342",
  day =          "15",
  month =        sep,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:30 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/S0377042702003643",
  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: Gautschi:2002:GQA
author: W. Gautschi
title: Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions
journal: j-J-COMPUT-APPL-MATH
volume: 139
number: 1
pages: 173--187
day: 1
month: feb
monthnumber: 2
year: 2002
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 33F05 (33C05 33C15 65D20)
MRnumber: MR1876879 (2002m:33029)
bibdate: Thu Dec 01 09:11:13 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 09:11:13 ???
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: W. Gautschi
rawtitle: {Gauss} quadrature approximations to hypergeometric and confluent hypergeometric functions
remark:
The paper treats ordinary and confluent hypergeometric functions $_2 F_1$ and $_1 F_1$, using their integral representations to obtain Gaussian quadrature rules.

entry:
@Article{Gautschi:2002:GQA,
  author =       "W. Gautschi",
  title =        "{Gauss} quadrature approximations to hypergeometric
                 and confluent hypergeometric functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "139",
  number =       "1",
  pages =        "173--187",
  day =          "1",
  month =        feb,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "33F05 (33C05 33C15 65D20)",
  MRnumber =     "MR1876879 (2002m:33029)",
  bibdate =      "Thu Dec 01 09:11:13 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  remark =       "The paper treats ordinary and confluent hypergeometric
                 functions $_2 F_1$ and $_1 F_1$, using their integral
                 representations to obtain Gaussian quadrature rules.",
}


bibtype: article
filename: elefunt.bib
label: Gil:2002:AAB
author: Amparo Gil and Javier Segura and Nico M. Temme
title: Algorithm 819: AIZ, BIZ: two Fortran 77 routines for the computation of complex Airy functions
journal: j-TOMS
volume: 28
number: 3
pages: 325--336
month: sep
monthnumber: 9
year: 2002
CODEN: ACMSCU
DOI: https://doi.org/10.1145/569147.569150
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Nov 9 11:16:50 MST 2002
bibtimestamp: 2002.11.09 11:16:50 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
abstract:
Two Fortran 77 routines for the evaluation of Airy functions of complex arguments $ A i(z) $, $ B i(z) $ and their derivatives are presented. The routines are based on the use of Gaussian quadrature, Maclaurin series and asymptotic expansions. Comparison with a previous code by D. E. Amos (ACM TOMS 12 (1986)) is provided.

rawabstract:
Two Fortran 77 routines for the evaluation of Airy functions of complex arguments $ A i(z) $, $ B i(z) $ and their derivatives are presented. The routines are based on the use of Gaussian quadrature, Maclaurin series and asymptotic expansions. Comparison with a previous code by D. E. Amos (ACM TOMS 12 (1986)) is provided.

rawtitle:
{Algorithm 819}: {AIZ}, {BIZ}: two {Fortran 77} routines for the computation of complex {Airy} functions

entry:
@Article{Gil:2002:AAB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 819}: {AIZ}, {BIZ}: two {Fortran 77}
                 routines for the computation of complex {Airy}
                 functions",
  journal =      j-TOMS,
  volume =       "28",
  number =       "3",
  pages =        "325--336",
  month =        sep,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/569147.569150",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 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 =     "Two Fortran 77 routines for the evaluation of Airy
                 functions of complex arguments $ A i(z) $, $ B i(z) $
                 and their derivatives are presented. The routines are
                 based on the use of Gaussian quadrature, Maclaurin
                 series and asymptotic expansions. Comparison with a
                 previous code by D. E. Amos (ACM TOMS 12 (1986)) is
                 provided.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Gil:2002:AGH
author: Amparo Gil and Javier Segura and Nico M. Temme
title: Algorithm 822: GIZ, HIZ: two Fortran 77 routines for the computation of complex Scorer functions
journal: j-TOMS
volume: 28
number: 4
pages: 436--447
month: dec
monthnumber: 12
year: 2002
CODEN: ACMSCU
DOI: https://doi.org/10.1145/592843.592847
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Fri Mar 28 08:17:55 MST 2003
bibtimestamp: 2003.03.28 08:17:55 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
abstract:
Two Fortran 77 routines for the evaluation of Scorer functions of complex arguments $ G i(z) $, $ H i(z) $ and their derivatives are presented. The routines are based on the use of quadrature, Maclaurin series and asymptotic expansions. For real $z$ comparison with a previous code by A. J. Macleod (J. Comput. Appl. Math. 53 (1994)) is provided.

rawabstract:
Two Fortran 77 routines for the evaluation of Scorer functions of complex arguments $ G i(z) $, $ H i(z) $ and their derivatives are presented. The routines are based on the use of quadrature, Maclaurin series and asymptotic expansions. For real $z$ comparison with a previous code by A. J. Macleod (J. Comput. Appl. Math. 53 (1994)) is provided.

rawtitle:
{Algorithm 822}: {GIZ}, {HIZ}: two {Fortran} 77 routines for the computation of complex {Scorer} functions

entry:
@Article{Gil:2002:AGH,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 822}: {GIZ}, {HIZ}: two {Fortran} 77
                 routines for the computation of complex {Scorer}
                 functions",
  journal =      j-TOMS,
  volume =       "28",
  number =       "4",
  pages =        "436--447",
  month =        dec,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/592843.592847",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  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 =     "Two Fortran 77 routines for the evaluation of Scorer
                 functions of complex arguments $ G i(z) $, $ H i(z) $
                 and their derivatives are presented. The routines are
                 based on the use of quadrature, Maclaurin series and
                 asymptotic expansions. For real $z$ comparison with a
                 previous code by A. J. Macleod (J. Comput. Appl. Math.
                 53 (1994)) is provided.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: techreport
filename: elefunt.bib
label: Gil:2002:CSF
author: A. Gil and J. Segura and N. M. Temme
title: Computing special functions by using quadrature rules
type: Report
number: MAS-R0230
institution: pub-CWI
address: pub-CWI:adr
pages: 11
year: 2002
LCCN: QA9.A1 R426 MAS-R0230
bibdate: Sat Oct 30 19:13:12 2010
bibsource: http://cat.cisti-icist.nrc-cnrc.gc.ca/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:13:12 ???
note: Published in cite Gil:2003:CSF.
acknowledgement: ack-nhfb
rawauthor: A. Gil and J. Segura and N. M. Temme
rawnote: Published in \cite{Gil:2003:CSF}.
rawtitle: Computing special functions by using quadrature rules
entry:
@TechReport{Gil:2002:CSF,
  author =       "A. Gil and J. Segura and N. M. Temme",
  title =        "Computing special functions by using quadrature
                 rules",
  type =         "Report",
  number =       "MAS-R0230",
  institution =  pub-CWI,
  address =      pub-CWI:adr,
  pages =        "11",
  year =         "2002",
  LCCN =         "QA9.A1 R426 MAS-R0230",
  bibdate =      "Sat Oct 30 19:13:12 2010",
  bibsource =    "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Gil:2003:CSF}.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Gil:2002:EMB
author: Amparo Gil and Javier Segura and Nico M. Temme
title: Evaluation of the Modified Bessel Function of the Third Kind of Imaginary Orders
journal: j-J-COMPUT-PHYS
volume: 175
number: 2
pages: 398--411
day: 20
month: jan
monthnumber: 1
year: 2002
CODEN: JCTPAH
DOI: https://doi.org/10.1006/jcph.2001.6894
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Jan 2 22:12:13 MST 2012
bibtimestamp: 2012.01.02 22:12:13 MST
URL: http://www.sciencedirect.com/science/article/pii/S0021999101968949
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
rawtitle: Evaluation of the Modified {Bessel} Function of the Third Kind of Imaginary Orders
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib

abstract:
The evaluation of the modified Bessel function of the third kind of purely imaginary order $ mathrm K_ia(x) $ is discussed; we also present analogous results for the derivative. The methods are based on the use of Maclaurin series, nonoscillatory integral representations, asymptotic expansions, and a continued fraction method, depending on the ranges of x and a. We discuss the range of applicability of the different approaches considered and conclude that power series, the continued fraction method, and the nonoscillatory integral representation can be used to accurately compute the function $ mathrm K_ia(x) $ in the range $ 0 leq a leq 200 $, $ 0 leq x leq 100 $; using a similar scheme the derivative $ mathrm K'_ia(x) $ can also be computed within these ranges.

rawabstract:
The evaluation of the modified Bessel function of the third kind of purely imaginary order $ \mathrm {K}_{ia}(x) $ is discussed; we also present analogous results for the derivative. The methods are based on the use of Maclaurin series, nonoscillatory integral representations, asymptotic expansions, and a continued fraction method, depending on the ranges of x and a. We discuss the range of applicability of the different approaches considered and conclude that power series, the continued fraction method, and the nonoscillatory integral representation can be used to accurately compute the function $ \mathrm {K}_{ia}(x) $ in the range $ 0 \leq a \leq 200 $, $ 0 \leq x \leq 100 $; using a similar scheme the derivative $ \mathrm {K}'_{ia(x)} $ can also be computed within these ranges.

entry:
@Article{Gil:2002:EMB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Evaluation of the Modified {Bessel} Function of the
                 Third Kind of Imaginary Orders",
  journal =      j-J-COMPUT-PHYS,
  volume =       "175",
  number =       "2",
  pages =        "398--411",
  day =          "20",
  month =        jan,
  year =         "2002",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1006/jcph.2001.6894",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 22:12:13 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021999101968949",
  abstract =     "The evaluation of the modified Bessel function of the
                 third kind of purely imaginary order $ \mathrm
                 {K}_{ia}(x) $ is discussed; we also present analogous
                 results for the derivative. The methods are based on
                 the use of Maclaurin series, nonoscillatory integral
                 representations, asymptotic expansions, and a continued
                 fraction method, depending on the ranges of x and a. We
                 discuss the range of applicability of the different
                 approaches considered and conclude that power series,
                 the continued fraction method, and the nonoscillatory
                 integral representation can be used to accurately
                 compute the function $ \mathrm {K}_{ia}(x) $ in the
                 range $ 0 \leq a \leq 200 $, $ 0 \leq x \leq 100 $;
                 using a similar scheme the derivative $ \mathrm
                 {K}'_{ia(x)} $ can also be computed within these
                 ranges.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Gray:2002:ARE
author: Norman Gray
title: Automatic reduction of elliptic integrals using Carlson's relations
journal: j-MATH-COMPUT
volume: 71
number: 237
pages: 311--318
month: jan
monthnumber: 1
year: 2002
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Thu Jan 31 06:16:28 MST 2002
bibsource: http://www.ams.org/mcom/2002-71-237; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.01.31 06:16:28 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Norman Gray
rawtitle: Automatic reduction of elliptic integrals using {Carlson}'s relations
URL:
http://www.ams.org/journal-getitem?pii=S0025-5718-01-01333-3; http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.dvi; http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.pdf; http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.ps; http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.tex

entry:
@Article{Gray:2002:ARE,
  author =       "Norman Gray",
  title =        "Automatic reduction of elliptic integrals using
                 {Carlson}'s relations",
  journal =      j-MATH-COMPUT,
  volume =       "71",
  number =       "237",
  pages =        "311--318",
  month =        jan,
  year =         "2002",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Thu Jan 31 06:16:28 MST 2002",
  bibsource =    "http://www.ams.org/mcom/2002-71-237;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/journal-getitem?pii=S0025-5718-01-01333-3;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.dvi;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.pdf;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.ps;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.tex",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Hassenpflug:2002:EAS
author: W. C. Hassenpflug
title: Error analysis in the series evaluation of the exponential type integral $ e^z E_1 (z) $
journal: j-COMPUT-MATH-APPL
volume: 43
number: 1--2
pages: 207--266
month: jan
monthnumber: 1
year: 2002
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:49:20 MST 2017
bibtimestamp: 2017.03.01 21:49:20 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122101002838
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: W. C. Hassenpflug
rawtitle: Error analysis in the series evaluation of the exponential type integral {$ e^z E_1 (z) $}
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Hassenpflug:2002:EAS,
  author =       "W. C. Hassenpflug",
  title =        "Error analysis in the series evaluation of the
                 exponential type integral {$ e^z E_1 (z) $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "43",
  number =       "1--2",
  pages =        "207--266",
  month =        jan,
  year =         "2002",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:20 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122101002838",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Kilbas:2002:ARH
author: Anatoly A. Kilbas and Luis Rodriguez and Juan J. Trujillo
title: Asymptotic representations for hypergeometric-Bessel type function and fractional integrals
journal: j-J-COMPUT-APPL-MATH
volume: 149
number: 2
pages: 469--487
day: 15
month: dec
monthnumber: 12
year: 2002
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:32 MST 2017
bibtimestamp: 2017.02.25 12:52:32 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702005629
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Anatoly A. Kilbas and Luis Rodr{\'\i}guez and Juan J. Trujillo
rawtitle: Asymptotic representations for hypergeometric-{Bessel} type function and fractional integrals
entry:
@Article{Kilbas:2002:ARH,
  author =       "Anatoly A. Kilbas and Luis Rodr{\'\i}guez and Juan J.
                 Trujillo",
  title =        "Asymptotic representations for hypergeometric-{Bessel}
                 type function and fractional integrals",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "149",
  number =       "2",
  pages =        "469--487",
  day =          "15",
  month =        dec,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:32 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/S0377042702005629",
  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: Korenev:2002:BFT
author: B. G. (Boris Grigorevich) Korenev
title: Bessel functions and their applications
publisher: pub-TAYLOR-FRANCIS
address: pub-TAYLOR-FRANCIS:adr
pages: ix + 276
year: 2002
ISBN: 0-415-28130-X (hardcover) OR 041528130X (hardcover)
ISBN13: 978-0-415-28130-0 (hardcover) OR 9780415281300 (hardcover)
LCCN: QA408 .K67 2002
bibdate: Sat Oct 30 17:01:51 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:01:51 MDT
series: Analytical methods and special functions
subject: Bessel functions
acknowledgement: ack-nhfb
rawauthor: B. G. (Boris Grigorevich) Korenev
rawtitle: {Bessel} functions and their applications
entry:
@Book{Korenev:2002:BFT,
  author =       "B. G. (Boris Grigorevich) Korenev",
  title =        "{Bessel} functions and their applications",
  publisher =    pub-TAYLOR-FRANCIS,
  address =      pub-TAYLOR-FRANCIS:adr,
  pages =        "ix + 276",
  year =         "2002",
  ISBN =         "0-415-28130-X (hardcover)",
  ISBN-13 =      "978-0-415-28130-0 (hardcover)",
  LCCN =         "QA408 .K67 2002",
  bibdate =      "Sat Oct 30 17:01:51 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  subject =      "Bessel functions",
  xxaddress =    pub-CRC:adr,
  xxpublisher =  pub-CRC,
}


bibtype: book
filename: elefunt.bib
label: Li:2002:SWF
author: Le-Wei Li and Xiao-Kang Kang and Mook-Seng Leong
title: Spheroidal Wave Functions in Electromagnetic Theory
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xiii + 295
year: 2002
ISBN: 0-471-03170-4 (hardcover) OR 0471031704 (hardcover)
ISBN13: 978-0-471-03170-3 (hardcover) OR 9780471031703 (hardcover)
LCCN: QC670 .L49 2002
bibdate: Sat Apr 1 14:32:29 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:32:29 MDT
series: Wiley series in microwave and optical engineering
subject: Electromagnetic theory; Spheroidal functions
acknowledgement: ack-nhfb
rawauthor: Le-Wei Li and Xiao-Kang Kang and Mook-Seng Leong
rawtitle: Spheroidal Wave Functions in Electromagnetic Theory
URL:
http://www.loc.gov/catdir/bios/wiley043/2001045399.html; http://www.loc.gov/catdir/description/wiley036/2001045399.html; http://www.loc.gov/catdir/toc/onix07/2001045399.html

TOC:
Preface Acknowledgments Introduction Spheroidal Coordinates and Wave Functions Dyadic Green's Functions in Spheroidal Systems EM Scattering by a Conducting Spheroid EM Scattering by a Coated Dielectric Spheroid Spheroidal Antennas SAR Distributions in a Spheroidal Head Model Analysis of Rainfall Attenuation Using Oblate Raindrops EM Eigenfrequencies in a Spheroidal Cavity Appendix A: Expressions of Spheroidal Vector Wave Functions Appendix B: Intermediates $I_t,ell ^mn(c)$ in Closed Form Appendix C: $cal U^q(i),t$ and $cal V^(i),t$ Used in the Matrix Equation System References Index

rawTOC:
Preface \\ Acknowledgments \\ Introduction \\ Spheroidal Coordinates and Wave Functions \\ Dyadic Green's Functions in Spheroidal Systems \\ EM Scattering by a Conducting Spheroid \\ EM Scattering by a Coated Dielectric Spheroid \\ Spheroidal Antennas \\ SAR Distributions in a Spheroidal Head Model \\ Analysis of Rainfall Attenuation Using Oblate Raindrops \\ EM Eigenfrequencies in a Spheroidal Cavity \\ Appendix A: Expressions of Spheroidal Vector Wave Functions \\ Appendix B: Intermediates $I_{t,\ell}^{mn}(c)$ in Closed Form \\ Appendix C: ${\cal U}^{q(i),t}$ and ${\cal V}^{(i),t}$ Used in the Matrix Equation System \\ References \\ Index

entry:
@Book{Li:2002:SWF,
  author =       "Le-Wei Li and Xiao-Kang Kang and Mook-Seng Leong",
  title =        "Spheroidal Wave Functions in Electromagnetic Theory",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiii + 295",
  year =         "2002",
  ISBN =         "0-471-03170-4 (hardcover)",
  ISBN-13 =      "978-0-471-03170-3 (hardcover)",
  LCCN =         "QC670 .L49 2002",
  bibdate =      "Sat Apr 1 14:32:29 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley series in microwave and optical engineering",
  URL =          "http://www.loc.gov/catdir/bios/wiley043/2001045399.html;
                 http://www.loc.gov/catdir/description/wiley036/2001045399.html;
                 http://www.loc.gov/catdir/toc/onix07/2001045399.html",
  acknowledgement = ack-nhfb,
  subject =      "Electromagnetic theory; Spheroidal functions",
  tableofcontents = "Preface \\
                 Acknowledgments \\
                 Introduction \\
                 Spheroidal Coordinates and Wave Functions \\
                 Dyadic Green's Functions in Spheroidal Systems \\
                 EM Scattering by a Conducting Spheroid \\
                 EM Scattering by a Coated Dielectric Spheroid \\
                 Spheroidal Antennas \\
                 SAR Distributions in a Spheroidal Head Model \\
                 Analysis of Rainfall Attenuation Using Oblate Raindrops
                 \\
                 EM Eigenfrequencies in a Spheroidal Cavity \\
                 Appendix A: Expressions of Spheroidal Vector Wave
                 Functions \\
                 Appendix B: Intermediates $I_{t,\ell}^{mn}(c)$ in
                 Closed Form \\
                 Appendix C: ${\cal U}^{q(i),t}$ and ${\cal V}^{(i),t}$
                 Used in the Matrix Equation System \\
                 References \\
                 Index",
}


bibtype: article
filename: elefunt.bib
label: McCluskey:2002:MLF
author: Glen McCluskey
title: Math Library Functions in C9X
journal: j-LOGIN
volume: 27
number: 2
pages: 8--13
month: apr
monthnumber: 4
year: 2002
CODEN: LOGNEM
ISSN: 1044-6397 OR 10446397
bibdate: Tue Apr 11 10:52:14 MDT 2006
bibtimestamp: 2006.04.11 10:52:14 MDT
URL: http://www.usenix.org/publications/login/2002-04/pdfs/mccluskey.pdf
fjournal: ;login: the USENIX Association newsletter
remark: This is a short tutorial on some of the new math library functions in C99.
acknowledgement: ack-nhfb
rawauthor: Glen McCluskey
rawtitle: Math Library Functions in {C9X}
bibsource:
http://www.usenix.org/publications/login/2002-04/index.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{McCluskey:2002:MLF,
  author =       "Glen McCluskey",
  title =        "Math Library Functions in {C9X}",
  journal =      j-LOGIN,
  volume =       "27",
  number =       "2",
  pages =        "8--13",
  month =        apr,
  year =         "2002",
  CODEN =        "LOGNEM",
  ISSN =         "1044-6397",
  bibdate =      "Tue Apr 11 10:52:14 MDT 2006",
  bibsource =    "http://www.usenix.org/publications/login/2002-04/index.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.usenix.org/publications/login/2002-04/pdfs/mccluskey.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     ";login: the USENIX Association newsletter",
  remark =       "This is a short tutorial on some of the new math
                 library functions in C99.",
}


bibtype: article
filename: elefunt.bib
label: Paris:2002:EBU
author: R. B. Paris
title: Error bounds for the uniform asymptotic expansion of the incomplete gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 147
number: 1
pages: 215--231
day: 1
month: oct
monthnumber: 10
year: 2002
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:30 MST 2017
bibtimestamp: 2017.02.25 12:52:30 MST
URL: http://www.sciencedirect.com/science/article/pii/S037704270200434X
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: R. B. Paris
rawtitle: Error bounds for the uniform asymptotic expansion of the incomplete gamma function
entry:
@Article{Paris:2002:EBU,
  author =       "R. B. Paris",
  title =        "Error bounds for the uniform asymptotic expansion of
                 the incomplete gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "147",
  number =       "1",
  pages =        "215--231",
  day =          "1",
  month =        oct,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:30 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/S037704270200434X",
  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: Paris:2002:UAE
author: R. B. Paris
title: A uniform asymptotic expansion for the incomplete gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 148
number: 2
pages: 323--339
month: nov
monthnumber: 11
year: 2002
CODEN: JCAMDI
DOI: https://doi.org/10.1016/s0377-0427(02)00553-8
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 18 09:18:08 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 09:18:08 ???
note: See related work cite Paris:2016:UAE.
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: R. B. Paris
rawnote: See related work \cite{Paris:2016:UAE}.
rawtitle: A uniform asymptotic expansion for the incomplete gamma function
entry:
@Article{Paris:2002:UAE,
  author =       "R. B. Paris",
  title =        "A uniform asymptotic expansion for the incomplete
                 gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "148",
  number =       "2",
  pages =        "323--339",
  month =        nov,
  year =         "2002",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/s0377-0427(02)00553-8",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 18 09:18:08 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See related work \cite{Paris:2016:UAE}.",
  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: Pineiro:2002:HRL
author: J.-A. Pineiro and M. D. Ercegovac and J. D. Bruguera
title: High-radix logarithm with selection by rounding
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 101--110
year: 2002
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: J.-A. Pineiro and M. D. Ercegovac and J. D. Bruguera
rawtitle: High-radix logarithm with selection by rounding
booktitle:
The IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2002. Proceedings. 17--19 July 2002

rawbooktitle:
{The IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2002. Proceedings. 17--19 July 2002}

entry:
@InProceedings{Pineiro:2002:HRL,
  author =       "J.-A. Pineiro and M. D. Ercegovac and J. D. Bruguera",
  booktitle =    "{The IEEE International Conference on
                 Application-Specific Systems, Architectures and
                 Processors, 2002. Proceedings. 17--19 July 2002}",
  title =        "High-radix logarithm with selection by rounding",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "101--110",
  year =         "2002",
  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 =      "A high-radix digit-recurrence algorithm or the
                 computation of the logarithm is presented in this
                 paper. Selection by rounding is used in iterations
                 j/spl ges/2, and selection by table in the first
                 iteration is combined with a restricted digit-set
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Pineiro:2002:HSD
author: J. A. Pineiro and J. D. Bruguera
journal: j-IEEE-TRANS-COMPUT
volume: 51
number: 12
pages: 1377--1388
month: dec
monthnumber: 12
year: 2002
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2002.1146704
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
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. A. Pi{\~n}eiro and J. D. Bruguera
title:
High-Speed Double Precision Computation of Reciprocal, Division, Square Root, and Inverse Square Root

rawtitle:
High-Speed Double Precision Computation of Reciprocal, Division, Square Root, and Inverse Square Root

entry:
@Article{Pineiro:2002:HSD,
  author =       "J. A. Pi{\~n}eiro and J. D. Bruguera",
  title =        "High-Speed Double Precision Computation of Reciprocal,
                 Division, Square Root, and Inverse Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "12",
  pages =        "1377--1388",
  month =        dec,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2002.1146704",
  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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A new method for the high-speed computation of
                 double-precision floating-point reciprocal, division,
                 square root, and inverse square root operations is
                 presented in this paper. This method employs a
                 second-degree minimax polynomial approximation to
                 \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Samko:2002:HIT
author: S. G. (Stefan Grigorevich) Samko
title: Hypersingular integrals and their applications
volume: 5
publisher: pub-TAYLOR-FRANCIS
address: pub-TAYLOR-FRANCIS:adr
pages: xvii + 359
year: 2002
ISBN: 0-415-27268-8 OR 0415272688
ISBN13: 978-0-415-27268-1 OR 9780415272681
LCCN: QA403.5 .S26 2002
bibdate: Sat Oct 30 17:22:10 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:22:10 MDT
series: Analytical methods and special functions
subject: singular integrals
acknowledgement: ack-nhfb
rawauthor: S. G. (Stefan Grigorevich) Samko
rawtitle: Hypersingular integrals and their applications
entry:
@Book{Samko:2002:HIT,
  author =       "S. G. (Stefan Grigorevich) Samko",
  title =        "Hypersingular integrals and their applications",
  volume =       "5",
  publisher =    pub-TAYLOR-FRANCIS,
  address =      pub-TAYLOR-FRANCIS:adr,
  pages =        "xvii + 359",
  year =         "2002",
  ISBN =         "0-415-27268-8",
  ISBN-13 =      "978-0-415-27268-1",
  LCCN =         "QA403.5 .S26 2002",
  bibdate =      "Sat Oct 30 17:22:10 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  subject =      "singular integrals",
}


bibtype: inproceedings
filename: elefunt.bib
label: Sawada:2002:FVD
author: J. Sawada
title: Formal verification of divide and square root algorithms using series calculation
crossref: Borrione:2002:TIW
pages: 31--49
year: 2002
bibdate: Fri Jun 24 15:14:00 2005
bibtimestamp: 2005.06.24 15:14:00 ???
acknowledgement: ack-nhfb
rawauthor: J. Sawada
rawtitle: Formal verification of divide and square root algorithms using series calculation
entry:
@InProceedings{Sawada:2002:FVD,
  author =       "J. Sawada",
  title =        "Formal verification of divide and square root
                 algorithms using series calculation",
  crossref =     "Borrione:2002:TIW",
  pages =        "31--49",
  year =         "2002",
  bibdate =      "Fri Jun 24 15:14:00 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Sawada:2002:MVS
author: Jun Sawada and Ruben Gamboa
title: Mechanical Verification of a Square Root Algorithm Using Taylor's Theorem
journal: j-LECT-NOTES-COMP-SCI
volume: 2517
pages: 274--??
year: 2002
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Nov 30 20:58:00 MST 2002
bibtimestamp: 2002.11.30 20:58:00 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Jun Sawada and Ruben Gamboa
rawtitle: Mechanical Verification of a Square Root Algorithm Using {Taylor}'s Theorem
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2517.htm; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://link.springer.de/link/service/series/0558/bibs/2517/25170274.htm; http://link.springer.de/link/service/series/0558/papers/2517/25170274.pdf

entry:
@Article{Sawada:2002:MVS,
  author =       "Jun Sawada and Ruben Gamboa",
  title =        "Mechanical Verification of a Square Root Algorithm
                 Using {Taylor}'s Theorem",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2517",
  pages =        "274--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Nov 30 20:58:00 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2517.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.de/link/service/series/0558/bibs/2517/25170274.htm;
                 http://link.springer.de/link/service/series/0558/papers/2517/25170274.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: misc
filename: elefunt.bib
label: Sebah:2002:IGF
author: Pascal Sebah and Xavier Gourdon
title: Introduction to the Gamma Function
pages: 274--??
day: 4
month: feb
monthnumber: 2
year: 2002
bibdate: Sat May 01 16:07:51 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.05.01 16:07:51 ???
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: Pascal Sebah and Xavier Gourdon
rawtitle: Introduction to the Gamma Function
URL:
http://numbers.computation.free.fr/Constants/constants.html; http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.ps

entry:
@Misc{Sebah:2002:IGF,
  author =       "Pascal Sebah and Xavier Gourdon",
  title =        "Introduction to the Gamma Function",
  howpublished = "World-Wide Web document",
  day =          "4",
  month =        feb,
  year =         "2002",
  bibdate =      "Sat May 01 16:07:51 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://numbers.computation.free.fr/Constants/constants.html;
                 http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.ps",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Shore:2002:RMM
author: Haim Shore
title: Response Modeling Methodology (RMM)-Exploring the Properties of the Implied Error Distribution
journal: j-COMMUN-STAT-THEORY-METH
volume: 31
number: 12
pages: 2225--2249
year: 2002
CODEN: CSTMDC
DOI: https://doi.org/10.1081/STA-120017223
ISSN: 0361-0926 (print), 1532-415X (electronic) OR 03610926 (print), 1532415X (electronic)
ISSNL: 0361-0926 OR 03610926
bibdate: Wed Jan 27 05:41:30 MST 2016
bibtimestamp: 2016.01.27 05:41:30 MST
fjournal: Communications in Statistics: Theory and Methods
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/lsta20
rawauthor: Haim Shore
rawtitle: Response Modeling Methodology ({RMM})-Exploring the Properties of the Implied Error Distribution
bibsource:
https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Shore:2002:RMM,
  author =       "Haim Shore",
  title =        "Response Modeling Methodology ({RMM})-Exploring the
                 Properties of the Implied Error Distribution",
  journal =      j-COMMUN-STAT-THEORY-METH,
  volume =       "31",
  number =       "12",
  pages =        "2225--2249",
  year =         "2002",
  CODEN =        "CSTMDC",
  DOI =          "https://doi.org/10.1081/STA-120017223",
  ISSN =         "0361-0926 (print), 1532-415X (electronic)",
  ISSN-L =       "0361-0926",
  bibdate =      "Wed Jan 27 05:41:30 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Theory and Methods",
  journal-URL =  "http://www.tandfonline.com/loi/lsta20",
}


bibtype: article
filename: elefunt.bib
label: Tornaria:2002:SRM
author: Gonzalo Tornaria
title: Square Roots Modulo $p$
journal: j-LECT-NOTES-COMP-SCI
volume: 2286
pages: 430--??
year: 2002
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:09:12 MDT 2002
bibtimestamp: 2002.09.10 19:09:12 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Gonzalo Tornar{\'\i}a
rawtitle: Square Roots Modulo $p$
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2286.htm; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2286/22860430.htm; http://link.springer-ny.com/link/service/series/0558/papers/2286/22860430.pdf

entry:
@Article{Tornaria:2002:SRM,
  author =       "Gonzalo Tornar{\'\i}a",
  title =        "Square Roots Modulo $p$",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2286",
  pages =        "430--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:12 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2286.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2286/22860430.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2286/22860430.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: book
filename: elefunt.bib
label: Vladimirov:2002:MTG
author: V. S. (Vasilii Sergeevich) Vladimirov
title: Methods of the theory of generalized functions
volume: 6
publisher: pub-TAYLOR-FRANCIS
address: pub-TAYLOR-FRANCIS:adr
pages: xiv + 311
year: 2002
ISBN: 0-415-27356-0 OR 0415273560
ISBN13: 978-0-415-27356-5 OR 9780415273565
LCCN: QC20.7.T45 V53 2002
bibdate: Sat Oct 30 17:22:15 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:22:15 MDT
series: Analytical methods and special functions
subject: Theory of distributions (Functional analysis); Integral transforms; Mathematical physics
acknowledgement: ack-nhfb
rawauthor: V. S. (Vasilii Sergeevich) Vladimirov
rawtitle: Methods of the theory of generalized functions
entry:
@Book{Vladimirov:2002:MTG,
  author =       "V. S. (Vasilii Sergeevich) Vladimirov",
  title =        "Methods of the theory of generalized functions",
  volume =       "6",
  publisher =    pub-TAYLOR-FRANCIS,
  address =      pub-TAYLOR-FRANCIS:adr,
  pages =        "xiv + 311",
  year =         "2002",
  ISBN =         "0-415-27356-0",
  ISBN-13 =      "978-0-415-27356-5",
  LCCN =         "QC20.7.T45 V53 2002",
  bibdate =      "Sat Oct 30 17:22:15 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  subject =      "Theory of distributions (Functional analysis);
                 Integral transforms; Mathematical physics",
}


bibtype: article
filename: elefunt.bib
label: Aarts:2003:ASF
author: Ronald M. Aarts and Augustus J. E. M. Janssen
title: Approximation of the Struve function $ H_1 $ occurring in impedance calculations
journal: j-J-ACOUST-SOC-AM
volume: 113
number: 5
pages: 2635--2637
month: may
monthnumber: 5
year: 2003
CODEN: JASMAN
DOI: https://doi.org/10.1121/1.1564019
ISSN: 0001-4966 OR 00014966
ISSNL: 0001-4966 OR 00014966
bibdate: Tue Mar 28 07:23:10 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.28 07:23:10 ???
fjournal: Journal of the Acoustical Society of America
acknowledgement: ack-nhfb
journalURL: http://scitation.aip.org/content/asa/journal/jasa
rawauthor: Ronald M. Aarts and Augustus J. E. M. Janssen
rawtitle: Approximation of the {Struve} function {$ H_1 $} occurring in impedance calculations
entry:
@Article{Aarts:2003:ASF,
  author =       "Ronald M. Aarts and Augustus J. E. M. Janssen",
  title =        "Approximation of the {Struve} function {$ H_1 $}
                 occurring in impedance calculations",
  journal =      j-J-ACOUST-SOC-AM,
  volume =       "113",
  number =       "5",
  pages =        "2635--2637",
  month =        may,
  year =         "2003",
  CODEN =        "JASMAN",
  DOI =          "https://doi.org/10.1121/1.1564019",
  ISSN =         "0001-4966",
  ISSN-L =       "0001-4966",
  bibdate =      "Tue Mar 28 07:23:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Acoustical Society of America",
  journal-URL =  "http://scitation.aip.org/content/asa/journal/jasa",
}


bibtype: article
filename: elefunt.bib
label: Abad:2003:AEQ
author: J. Abad and J. Sesma
title: Asymptotic expansion of the quasiconfluent hypergeometric function
journal: j-J-MATH-PHYS
volume: 44
number: 4
pages: 1723--1729
month: apr
monthnumber: 4
year: 2003
CODEN: JMAPAQ
ISSNL: 0022-2488 OR 00222488
bibdate: Tue Dec 16 11:36:01 MST 2003
bibtimestamp: 2003.12.16 11:36:01 MST
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: J. Abad and J. Sesma
rawtitle: Asymptotic expansion of the quasiconfluent hypergeometric function
bibsource:
http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib

entry:
@Article{Abad:2003:AEQ,
  author =       "J. Abad and J. Sesma",
  title =        "Asymptotic expansion of the quasiconfluent
                 hypergeometric function",
  journal =      j-J-MATH-PHYS,
  volume =       "44",
  number =       "4",
  pages =        "1723--1729",
  month =        apr,
  year =         "2003",
  CODEN =        "JMAPAQ",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Tue Dec 16 11:36:01 MST 2003",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
}


bibtype: article
filename: elefunt.bib
label: Agou:2003:SPR
author: Simon Joseph Agou and Marc Deleglise and Jean-Louis Nicolas
title: Short Polynomial Representations for Square Roots Modulo $p$
journal: j-DESIGNS-CODES-CRYPTOGR
volume: 28
number: 1
pages: 33--44
month: jan
monthnumber: 1
year: 2003
CODEN: DCCREC
ISSN: 0925-1022 (print), 1573-7586 (electronic) OR 09251022 (print), 15737586 (electronic)
ISSNL: 0925-1022 OR 09251022
bibdate: Thu Dec 11 06:27:20 MST 2003
bibtimestamp: 2003.12.11 06:27:20 MST
fjournal: Designs, codes, and cryptography
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10623
rawauthor: Simon Joseph Agou and Marc Del{\'e}glise and Jean-Louis Nicolas
rawtitle: Short Polynomial Representations for Square Roots Modulo $p$
bibsource:
http://www.wkap.nl/jrnltoc.htm/0925-1022; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/fulltext.pdf

entry:
@Article{Agou:2003:SPR,
  author =       "Simon Joseph Agou and Marc Del{\'e}glise and
                 Jean-Louis Nicolas",
  title =        "Short Polynomial Representations for Square Roots
                 Modulo $p$",
  journal =      j-DESIGNS-CODES-CRYPTOGR,
  volume =       "28",
  number =       "1",
  pages =        "33--44",
  month =        jan,
  year =         "2003",
  CODEN =        "DCCREC",
  ISSN =         "0925-1022 (print), 1573-7586 (electronic)",
  ISSN-L =       "0925-1022",
  bibdate =      "Thu Dec 11 06:27:20 MST 2003",
  bibsource =    "http://www.wkap.nl/jrnltoc.htm/0925-1022;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Designs, codes, and cryptography",
  journal-URL =  "http://link.springer.com/journal/10623",
}


bibtype: article
filename: elefunt.bib
label: Alzer:2003:GHM
author: Horst Alzer
title: On Gautschi's harmonic mean inequality for the gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 157
number: 1
pages: 243--249
day: 1
month: aug
monthnumber: 8
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:37 MST 2017
bibtimestamp: 2017.02.25 12:52:37 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042703004564
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Horst Alzer
rawtitle: On {Gautschi}'s harmonic mean inequality for the gamma function
entry:
@Article{Alzer:2003:GHM,
  author =       "Horst Alzer",
  title =        "On {Gautschi}'s harmonic mean inequality for the gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "157",
  number =       "1",
  pages =        "243--249",
  day =          "1",
  month =        aug,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:37 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/S0377042703004564",
  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: Beaumont:2003:BSE
author: James Beaumont and Russell Bradford and James H. Davenport
booktitle: Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation
title: Better simplification of elementary functions through power series
publisher: pub-ACM
address: pub-ACM:adr
pages: 30--36 (electronic)
year: 2003
MRclass: 33F10 (68W30)
MRnumber: MR2035192 (2005e:33018)
MRreviewer: Ekatherina A. Karatsuba
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 ???
acknowledgement: ack-nhfb
rawauthor: James Beaumont and Russell Bradford and James H. Davenport
rawbooktitle: Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation
rawtitle: Better simplification of elementary functions through power series
remark:
A new algorithm testing the correctness of simplifications of elementary functions in the presence of branch cuts is proposed.

entry:
@InProceedings{Beaumont:2003:BSE,
  author =       "James Beaumont and Russell Bradford and James H.
                 Davenport",
  booktitle =    "Proceedings of the 2003 International Symposium on
                 Symbolic and Algebraic Computation",
  title =        "Better simplification of elementary functions through
                 power series",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "30--36 (electronic)",
  year =         "2003",
  MRclass =      "33F10 (68W30)",
  MRnumber =     "MR2035192 (2005e:33018)",
  MRreviewer =   "Ekatherina A. Karatsuba",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "A new algorithm testing the correctness of
                 simplifications of elementary functions in the presence
                 of branch cuts is proposed.",
}


bibtype: article
filename: elefunt.bib
label: Buhring:2003:PSH
author: Wolfgang Buhring
title: Partial sums of hypergeometric functions of unit argument
journal: j-PROC-AM-MATH-SOC
volume: 132
number: 2
pages: 407--415
year: 2003
CODEN: PAMYAR
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 33C20
MRnumber: MR2022363 (2005f:33011)
bibdate: Thu Dec 01 09:53:54 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 09:53:54 ???
fjournal: Proceedings of the American Mathematical Society
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/journals/proc
rawauthor: Wolfgang B{\"u}hring
rawtitle: Partial sums of hypergeometric functions of unit argument
entry:
@Article{Buhring:2003:PSH,
  author =       "Wolfgang B{\"u}hring",
  title =        "Partial sums of hypergeometric functions of unit
                 argument",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "132",
  number =       "2",
  pages =        "407--415",
  month =        "????",
  year =         "2003",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "33C20",
  MRnumber =     "MR2022363 (2005f:33011)",
  bibdate =      "Thu Dec 01 09:53:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}


bibtype: article
filename: elefunt.bib
label: Chiani:2003:NEB
author: M. Chiani and D. Dardari and M. K. Simon
journal: j-IEEE-TRANS-WIREL-COMMUN
volume: 24
number: 5
pages: 840--845
month: may
monthnumber: 5
year: 2003
CODEN: ITWCAX
DOI: https://doi.org/10.1109/twc.2003.814350
ISSN: 1536-1276 (print), 1558-2248 (electronic) OR 15361276 (print), 15582248 (electronic)
ISSNL: 1536-1276 OR 15361276
bibdate: Sat Dec 16 15:47:42 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 15:47:42 ???
URL: http://ieeexplore.ieee.org/document/1210748/
fjournal: IEEE Transactions on Wireless Communications
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7693
rawauthor: M. Chiani and D. Dardari and M. K. Simon
title:
New exponential bounds and approximations for the computation of error probability in fading channels

rawtitle:
New exponential bounds and approximations for the computation of error probability in fading channels

entry:
@Article{Chiani:2003:NEB,
  author =       "M. Chiani and D. Dardari and M. K. Simon",
  title =        "New exponential bounds and approximations for the
                 computation of error probability in fading channels",
  journal =      j-IEEE-TRANS-WIREL-COMMUN,
  volume =       "24",
  number =       "5",
  pages =        "840--845",
  month =        may,
  year =         "2003",
  CODEN =        "ITWCAX",
  DOI =          "https://doi.org/10.1109/twc.2003.814350",
  ISSN =         "1536-1276 (print), 1558-2248 (electronic)",
  ISSN-L =       "1536-1276",
  bibdate =      "Sat Dec 16 15:47:42 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/1210748/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Wireless Communications",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7693",
}


bibtype: techreport
filename: elefunt.bib
label: Cornea:2003:DSR
author: M. Cornea and J. Harrison and C. Iordache and B. Norin and S. Story
title: Division, Square Root and Remainder Algorithms for the Intel Itanium Architecture
type: Report
institution: pub-INTEL
address: pub-INTEL:adr
pages: 840--845
month: nov
monthnumber: 11
year: 2003
bibdate: Fri Jun 24 12:05:58 2005
bibtimestamp: 2005.06.24 12:05:58 ???
acknowledgement: ack-nhfb
rawauthor: M. Cornea and J. Harrison and C. Iordache and B. Norin and S. Story
rawtitle: Division, Square Root and Remainder Algorithms for the {Intel Itanium} Architecture
entry:
@TechReport{Cornea:2003:DSR,
  author =       "M. Cornea and J. Harrison and C. Iordache and B. Norin
                 and S. Story",
  title =        "Division, Square Root and Remainder Algorithms for the
                 {Intel Itanium} Architecture",
  type =         "Report",
  institution =  pub-INTEL,
  address =      pub-INTEL:adr,
  month =        nov,
  year =         "2003",
  bibdate =      "Fri Jun 24 12:05:58 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Coussement:2003:AMO
author: Els Coussement and Walter Van Assche
journal: j-J-COMPUT-APPL-MATH
volume: 153
number: 1--2
pages: 141--149
day: 1
month: apr
monthnumber: 4
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:34 MST 2017
bibtimestamp: 2017.02.25 12:52:34 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702005964
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Els Coussement and Walter {Van Assche}
title:
Asymptotics of multiple orthogonal polynomials associated with the modified Bessel functions of the first kind

rawtitle:
Asymptotics of multiple orthogonal polynomials associated with the modified {Bessel} functions of the first kind

entry:
@Article{Coussement:2003:AMO,
  author =       "Els Coussement and Walter {Van Assche}",
  title =        "Asymptotics of multiple orthogonal polynomials
                 associated with the modified {Bessel} functions of the
                 first kind",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "153",
  number =       "1--2",
  pages =        "141--149",
  day =          "1",
  month =        apr,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:34 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/S0377042702005964",
  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: Dominici:2003:NDS
author: Diego Dominici
title: Nested derivatives: a simple method for computing series expansions of inverse functions
journal: j-INT-J-MATH-MATH-SCI
volume: 58
pages: 3699--3715
year: 2003
ISSN: 0161-1712 (print), 1687-0425 (electronic) OR 01611712 (print), 16870425 (electronic)
ISSNL: 0161-1712 OR 01611712
MRclass: 41A58 (33F10)
MRnumber: MR2031140 (2005f:41079)
MRreviewer: Tord H. Ganelius
bibdate: Mon Oct 24 11:37:20 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.10.24 11:37:20 ???
URL: http://www2.newpaltz.edu/~dominicd/NESTED14.pdf
fjournal: International Journal of Mathematics and Mathematical Sciences
acknowledgement: ack-nhfb
journalURL: https://www.hindawi.com/journals/ijmms/
rawauthor: Diego Dominici
rawtitle: Nested derivatives: a simple method for computing series expansions of inverse functions
abstract:
We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating the inverses of some special functions.

keywords:
error function, erf(x); incomplete beta function, B(nu,mu,x); incomplete gamma function, gamma(nu,x); logarithm integral, li(x); Maple; sine integral, Si(x)

rawabstract:
We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating the inverses of some special functions.

entry:
@Article{Dominici:2003:NDS,
  author =       "Diego Dominici",
  title =        "Nested derivatives: a simple method for computing
                 series expansions of inverse functions",
  journal =      j-INT-J-MATH-MATH-SCI,
  volume =       "58",
  pages =        "3699--3715",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "0161-1712 (print), 1687-0425 (electronic)",
  ISSN-L =       "0161-1712",
  MRclass =      "41A58 (33F10)",
  MRnumber =     "MR2031140 (2005f:41079)",
  MRreviewer =   "Tord H. Ganelius",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www2.newpaltz.edu/~dominicd/NESTED14.pdf",
  abstract =     "We give an algorithm to compute the series expansion
                 for the inverse of a given function. The algorithm is
                 extremely easy to implement and gives the first $N$
                 terms of the series. We show several examples of its
                 application in calculating the inverses of some special
                 functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
  journal-URL =  "https://www.hindawi.com/journals/ijmms/",
  keywords =     "error function, erf(x); incomplete beta function,
                 B(nu,mu,x); incomplete gamma function, gamma(nu,x);
                 logarithm integral, li(x); Maple; sine integral,
                 Si(x)",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ercegovac:2003:DRA
author: M. D. Ercegovac and J.-M. Muller
booktitle: Conference Record of the Thirty-Seventh Asilomar Conference on Signals, Systems and Computers, 2003
title: Digit-recurrence algorithms for division and square root with limited precision primitives
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1440--1444
year: 2003
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: M. D. Ercegovac and J.-M. Muller
rawbooktitle: Conference Record of the Thirty-Seventh Asilomar Conference on Signals, Systems and Computers, 2003
rawtitle: Digit-recurrence algorithms for division and square root with limited precision primitives
entry:
@InProceedings{Ercegovac:2003:DRA,
  author =       "M. D. Ercegovac and J.-M. Muller",
  booktitle =    "Conference Record of the Thirty-Seventh Asilomar
                 Conference on Signals, Systems and Computers, 2003",
  title =        "Digit-recurrence algorithms for division and square
                 root with limited precision primitives",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1440--1444",
  year =         "2003",
  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 =      "We propose a digit-recurrence algorithm for square
                 root using limited-precision multipliers, adders, and
                 table-lookups. The algorithm, except in the
                 initialization, uses the digit-recurrence algorithm for
                 division with limited-precision primitives \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Fabijonas:2003:ACM
author: B. R. Fabijonas and Daniel W. Lozier and J. M. Rappoport
title: Algorithms and Codes for the Macdonald Function: Recent Progress and Comparisons
journal: j-J-COMPUT-APPL-MATH
volume: 161
number: 1
pages: 179--192
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 33F05 (33C10 65D20)
MRnumber: MR2018582
bibdate: Fri Jul 09 06:21:51 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:21:51 ???
URL: http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6596.ps
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: B. R. Fabijonas and Daniel W. Lozier and J. M. Rappoport
rawtitle: Algorithms and Codes for the {Macdonald} Function: Recent Progress and Comparisons
entry:
@Article{Fabijonas:2003:ACM,
  author =       "B. R. Fabijonas and Daniel W. Lozier and J. M.
                 Rappoport",
  title =        "Algorithms and Codes for the {Macdonald} Function:
                 Recent Progress and Comparisons",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "161",
  number =       "1",
  pages =        "179--192",
  month =        "????",
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "33F05 (33C10 65D20)",
  MRnumber =     "MR2018582",
  bibdate =      "Fri Jul 09 06:21:51 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6596.ps",
  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: Galue:2003:FRG
author: L. Galue and A. Al-Zamel and Shyam L. Kalla
title: Further results on generalized hypergeometric functions
journal: j-APPL-MATH-COMP
volume: 136
number: 1
pages: 17--25
day: 25
month: mar
monthnumber: 3
year: 2003
CODEN: AMHCBQ
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Fri Jan 9 08:40:52 MST 2004
bibtimestamp: 2004.01.09 08:40:52 MST
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: L. Galu{\'e} and A. Al-Zamel and Shyam L. Kalla
rawtitle: Further results on generalized hypergeometric functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Galue:2003:FRG,
  author =       "L. Galu{\'e} and A. Al-Zamel and Shyam L. Kalla",
  title =        "Further results on generalized hypergeometric
                 functions",
  journal =      j-APPL-MATH-COMP,
  volume =       "136",
  number =       "1",
  pages =        "17--25",
  day =          "25",
  month =        mar,
  year =         "2003",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Jan 9 08:40:52 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:2003:EEI
author: W. Gautschi and F. E. Harris and N. M. Temme
title: Expansions of the exponential integral in incomplete gamma functions
journal: j-APPL-MATH-LETT
volume: 16
number: 7
pages: 1095--1099
month: oct
monthnumber: 10
year: 2003
CODEN: AMLEEL
DOI: https://doi.org/10.1016/S0893-9659(03)90100-5
ISSN: 0893-9659 (print), 1873-5452 (electronic) OR 08939659 (print), 18735452 (electronic)
ISSNL: 0893-9659 OR 08939659
MRclass: 33B20
bibdate: Wed Dec 4 10:29:43 2013
bibtimestamp: 2013.12.04 10:29:43 ???
fjournal: Applied Mathematics Letters
ZMnumber: 1058.33002
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08939659
rawauthor: W. Gautschi and F. E. Harris and N. M. Temme
rawtitle: Expansions of the exponential integral in incomplete gamma functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Gautschi:2003:EEI,
  author =       "W. Gautschi and F. E. Harris and N. M. Temme",
  title =        "Expansions of the exponential integral in incomplete
                 gamma functions",
  journal =      j-APPL-MATH-LETT,
  volume =       "16",
  number =       "7",
  pages =        "1095--1099",
  month =        oct,
  year =         "2003",
  CODEN =        "AMLEEL",
  DOI =          "https://doi.org/10.1016/S0893-9659(03)90100-5",
  ISSN =         "0893-9659 (print), 1873-5452 (electronic)",
  ISSN-L =       "0893-9659",
  MRclass =      "33B20",
  bibdate =      "Wed Dec 4 10:29:43 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "1058.33002",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08939659",
}


bibtype: article
filename: elefunt.bib
label: Gil:2003:CMB
author: Amparo Gil and Javier Segura and Nico M. Temme
journal: j-J-COMPUT-APPL-MATH
volume: 153
number: 1--2
pages: 225--234
day: 1
month: apr
monthnumber: 4
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:34 MST 2017
bibtimestamp: 2017.02.25 12:52:34 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702006088
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
title:
Computation of the modified Bessel function of the third kind of imaginary orders: uniform Airy-type asymptotic expansion

rawtitle:
Computation of the modified {Bessel} function of the third kind of imaginary orders: uniform {Airy}-type asymptotic expansion

entry:
@Article{Gil:2003:CMB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computation of the modified {Bessel} function of the
                 third kind of imaginary orders: uniform {Airy}-type
                 asymptotic expansion",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "153",
  number =       "1--2",
  pages =        "225--234",
  day =          "1",
  month =        apr,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:34 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/S0377042702006088",
  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: Gil:2003:CSF
author: Amparo Gil and Javier Segura and Nico M. Temme
title: Computing Special Functions by Using Quadrature Rules
journal: j-NUMER-ALGORITHMS
volume: 33
number: 1--4
pages: 265--275
month: aug
monthnumber: 8
year: 2003
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Sep 29 08:37:11 MDT 2003
bibsource: http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2003.09.29 08:37:11 MDT
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
rawtitle: Computing Special Functions by Using Quadrature Rules
URL:
http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/fulltext.pdf

entry:
@Article{Gil:2003:CSF,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computing Special Functions by Using Quadrature
                 Rules",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "33",
  number =       "1--4",
  pages =        "265--275",
  month =        aug,
  year =         "2003",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Sep 29 08:37:11 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Harrison:2003:FVS
author: John Harrison
title: Formal verification of square root algorithms
journal: j-FORM-METHODS-SYST-DES
volume: 22
number: 2
pages: 143--153
month: mar
monthnumber: 3
year: 2003
CODEN: FMSDE6
DOI: https://doi.org/10.1023/A:1022973506233
ISSN: 0925-9856 (print), 1572-8102 (electronic) OR 09259856 (print), 15728102 (electronic)
ISSNL: 0925-9856 OR 09259856
bibdate: Sat Feb 08 08:47:21 2020
bibtimestamp: 2020.02.08 08:47:21 ???
URL: https://dl.acm.org/doi/abs/10.1023/A:1022973506233
fjournal: Formal Methods in System Design
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/fmsd
rawauthor: John Harrison
rawtitle: Formal verification of square root algorithms
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

abstract:
We discuss the formal verification of some low-level mathematical software for the Intel Itanium architecture. A number of important algorithms have been proven correct using the HOL Light theorem prover. After briefly surveying some of our formal verification work, we discuss in more detail the verification of a square root algorithm, which helps to illustrate why some features of HOL Light, in particular programmability, make it especially suitable for these applications.

rawabstract:
We discuss the formal verification of some low-level mathematical software for the Intel Itanium architecture. A number of important algorithms have been proven correct using the HOL Light theorem prover. After briefly surveying some of our formal verification work, we discuss in more detail the verification of a square root algorithm, which helps to illustrate why some features of HOL Light, in particular programmability, make it especially suitable for these applications.

entry:
@Article{Harrison:2003:FVS,
  author =       "John Harrison",
  title =        "Formal verification of square root algorithms",
  journal =      j-FORM-METHODS-SYST-DES,
  volume =       "22",
  number =       "2",
  pages =        "143--153",
  month =        mar,
  year =         "2003",
  CODEN =        "FMSDE6",
  DOI =          "https://doi.org/10.1023/A:1022973506233",
  ISSN =         "0925-9856 (print), 1572-8102 (electronic)",
  ISSN-L =       "0925-9856",
  bibdate =      "Sat Feb 08 08:47:21 2020",
  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",
  URL =          "https://dl.acm.org/doi/abs/10.1023/A:1022973506233",
  abstract =     "We discuss the formal verification of some low-level
                 mathematical software for the Intel Itanium
                 architecture. A number of important algorithms have
                 been proven correct using the HOL Light theorem prover.
                 After briefly surveying some of our formal verification
                 work, we discuss in more detail the verification of a
                 square root algorithm, which helps to illustrate why
                 some features of HOL Light, in particular
                 programmability, make it especially suitable for these
                 applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "Formal Methods in System Design",
  journal-URL =  "https://dl.acm.org/loi/fmsd",
}


bibtype: misc
filename: elefunt.bib
label: Intel:2003:DSR
author: Intel
title: Divide, Square Root, and Remainder Algorithms for the Itanium Architecture
pages: 143--153
day: 18
month: dec
monthnumber: 12
year: 2003
bibdate: Tue Nov 18 16:23:36 2008
bibtimestamp: 2008.11.18 16:23:36 ???
URL: http://www.intel.com/cd/software/products/asmo-na/eng/219863.htm
acknowledgement: ack-nhfb
howpublished: Intel Software Development Products
rawauthor: {Intel}
rawtitle: Divide, Square Root, and Remainder Algorithms for the {Itanium} Architecture
entry:
@Misc{Intel:2003:DSR,
  author =       "{Intel}",
  title =        "Divide, Square Root, and Remainder Algorithms for the
                 {Itanium} Architecture",
  howpublished = "Intel Software Development Products",
  day =          "18",
  month =        dec,
  year =         "2003",
  bibdate =      "Tue Nov 18 16:23:36 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.intel.com/cd/software/products/asmo-na/eng/219863.htm",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: elefunt.bib
label: Intel:2003:NID
author: Intel
pages: 143--153
day: 18
month: dec
monthnumber: 12
year: 2003
bibdate: Tue Nov 18 16:23:36 2008
bibtimestamp: 2008.11.18 16:23:36 ???
URL: http://www.intel.com/cd/software/products/asmo-na/eng/219864.htm
acknowledgement: ack-nhfb
howpublished: Intel Software Development Products
rawauthor: {Intel}
title:
Non-IEEE Division, Square Root, Reciprocal, and Reciprocal Square Root Algorithms for the Intel Itanium Architecture

rawtitle:
Non-{IEEE} Division, Square Root, Reciprocal, and Reciprocal Square Root Algorithms for the {Intel Itanium} Architecture

entry:
@Misc{Intel:2003:NID,
  author =       "{Intel}",
  title =        "Non-{IEEE} Division, Square Root, Reciprocal, and
                 Reciprocal Square Root Algorithms for the {Intel
                 Itanium} Architecture",
  howpublished = "Intel Software Development Products",
  day =          "18",
  month =        dec,
  year =         "2003",
  bibdate =      "Tue Nov 18 16:23:36 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.intel.com/cd/software/products/asmo-na/eng/219864.htm",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Kzaz:2003:CAG
author: M. Kzaz and M. Prevost
title: Convergence Acceleration of Gauss--Chebyshev Quadrature Formulae
journal: j-NUMER-ALGORITHMS
volume: 34
number: 2--4
pages: 379--391
month: dec
monthnumber: 12
year: 2003
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Tue Jan 13 17:32:50 MST 2004
bibsource: http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.01.13 17:32:50 MST
fjournal: Numerical Algorithms
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: M. Kzaz and M. Pr{\'e}vost
rawtitle: Convergence Acceleration of {Gauss--Chebyshev} Quadrature Formulae
URL:
http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/fulltext.pdf

entry:
@Article{Kzaz:2003:CAG,
  author =       "M. Kzaz and M. Pr{\'e}vost",
  title =        "Convergence Acceleration of {Gauss--Chebyshev}
                 Quadrature Formulae",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "34",
  number =       "2--4",
  pages =        "379--391",
  month =        dec,
  year =         "2003",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Tue Jan 13 17:32:50 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Lang:2003:RRS
author: Tomas Lang and Elisardo Antelo
title: Radix-$4$ Reciprocal Square-root and Its Combination with Division and Square Root
journal: j-IEEE-TRANS-COMPUT
volume: 52
number: 9
pages: 1100--1114
month: sep
monthnumber: 9
year: 2003
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2003.1228508
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
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Tom{\'a}s Lang and Elisardo Antelo
rawtitle: Radix-$4$ Reciprocal Square-root and Its Combination with Division and Square Root
abstract:
In this work, we present a reciprocal square root algorithm by digit recurrence and selection by a staircase function and the radix-$4$ implementation. As in similar algorithms for division and square root, the results are obtained correctly rounded in a straightforward manner (in contrast to existing methods to compute the reciprocal square root). Although, apparently, a single selection function can only be used for $ j geq 2 $ (the selection constants are different for $ j = 0 $, $ j = 1 $, and $ j geq 2 $ ), we show that it is possible to use a single selection function for all iterations. We perform a rough comparison with existing methods and we conclude that our implementation is a low hardware complexity solution with moderate latency, especially for exactly rounded results. We also extend the unit to support division and square root with the same selection function and with slight modifications in the initialization of the reciprocal square root unit.

rawabstract:
In this work, we present a reciprocal square root algorithm by digit recurrence and selection by a staircase function and the radix-$4$ implementation. As in similar algorithms for division and square root, the results are obtained correctly rounded in a straightforward manner (in contrast to existing methods to compute the reciprocal square root). Although, apparently, a single selection function can only be used for $ j \geq 2 $ (the selection constants are different for $ j = 0 $, $ j = 1 $, and $ j \geq 2 $ ), we show that it is possible to use a single selection function for all iterations. We perform a rough comparison with existing methods and we conclude that our implementation is a low hardware complexity solution with moderate latency, especially for exactly rounded results. We also extend the unit to support division and square root with the same selection function and with slight modifications in the initialization of the reciprocal square root unit.

entry:
@Article{Lang:2003:RRS,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  title =        "Radix-$4$ Reciprocal Square-root and Its Combination
                 with Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "9",
  pages =        "1100--1114",
  month =        sep,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1228508",
  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",
  abstract =     "In this work, we present a reciprocal square root
                 algorithm by digit recurrence and selection by a
                 staircase function and the radix-$4$ implementation. As
                 in similar algorithms for division and square root, the
                 results are obtained correctly rounded in a
                 straightforward manner (in contrast to existing methods
                 to compute the reciprocal square root). Although,
                 apparently, a single selection function can only be
                 used for $ j \geq 2 $ (the selection constants are
                 different for $ j = 0 $, $ j = 1 $, and $ j \geq 2 $ ),
                 we show that it is possible to use a single selection
                 function for all iterations. We perform a rough
                 comparison with existing methods and we conclude that
                 our implementation is a low hardware complexity
                 solution with moderate latency, especially for exactly
                 rounded results. We also extend the unit to support
                 division and square root with the same selection
                 function and with slight modifications in the
                 initialization of the reciprocal square root unit.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: elefunt.bib
label: Lefevre:2003:WCC
author: Vincent Lefevre and Jean-Michel Muller
title: Worst Cases for Correct Rounding for the Elementary Functions in Double Precision
type: Technical report
institution: INRIA, Projet Spaces, LORIA, Campus Scientifique
address: B.P. 239, 54506 Vandoeuvre-les-Nancy Cedex, France
pages: 1100--1114
day: 14
month: aug
monthnumber: 8
year: 2003
bibdate: Thu Jul 08 08:27:53 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.08 08:27:53 ???
URL: http://perso.ens-lyon.fr/jean-michel.muller/TMDworstcases.pdf
keywords: computer arithmetic; elementary functions; floating-point arithmetic; Table Maker's Dilemma
acknowledgement: ack-nhfb
rawauthor: Vincent Lef{\`e}vre and Jean-Michel Muller
rawtitle: Worst Cases for Correct Rounding for the Elementary Functions in Double Precision
abstract:
We give the results of our search for the worst cases for correct rounding of the major elementary functions in double precision floating-point arithmetic. These results allow the design of reasonably fast routines that will compute these functions with correct rounding, at least in some interval, for any of the four rounding modes specified by the IEEE-754 standard. They will also allow one to easily test libraries that are claimed to provide correctly rounded functions.

rawabstract:
We give the results of our search for the worst cases for correct rounding of the major elementary functions in double precision floating-point arithmetic. These results allow the design of reasonably fast routines that will compute these functions with correct rounding, at least in some interval, for any of the four rounding modes specified by the IEEE-754 standard. They will also allow one to easily test libraries that are claimed to provide correctly rounded functions.

entry:
@TechReport{Lefevre:2003:WCC,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller",
  title =        "Worst Cases for Correct Rounding for the Elementary
                 Functions in Double Precision",
  type =         "Technical report",
  institution =  "INRIA, Projet Spaces, LORIA, Campus Scientifique",
  address =      "B.P. 239, 54506 Vandoeuvre-l{\`e}s-Nancy Cedex,
                 France",
  day =          "14",
  month =        aug,
  year =         "2003",
  bibdate =      "Thu Jul 08 08:27:53 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://perso.ens-lyon.fr/jean-michel.muller/TMDworstcases.pdf",
  abstract =     "We give the results of our search for the worst cases
                 for correct rounding of the major elementary functions
                 in double precision floating-point arithmetic. These
                 results allow the design of reasonably fast routines
                 that will compute these functions with correct
                 rounding, at least in some interval, for any of the
                 four rounding modes specified by the IEEE-754 standard.
                 They will also allow one to easily test libraries that
                 are claimed to provide correctly rounded functions.",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic; elementary functions;
                 floating-point arithmetic; Table Maker's Dilemma",
}


bibtype: article
filename: elefunt.bib
label: Lozier:2003:NDL
author: Daniel W. Lozier
title: NIST Digital Library of Mathematical Functions
journal: j-ANN-MATH-ARTIF-INTELL
volume: 38
number: 1--3
pages: 105--119
month: may
monthnumber: 5
year: 2003
CODEN: AMAIEC
ISSN: 1012-2443 (print), 1573-7470 (electronic) OR 10122443 (print), 15737470 (electronic)
ISSNL: 1012-2443 OR 10122443
bibdate: Fri Jul 09 06:23:08 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:23:08 ???
URL: http://math.nist.gov/acmd/Staff/DLozier/publications/Linz01.ps
fjournal: Annals of Mathematics and Artificial Intelligence
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10472
rawauthor: Daniel W. Lozier
rawtitle: {NIST Digital Library of Mathematical Functions}
entry:
@Article{Lozier:2003:NDL,
  author =       "Daniel W. Lozier",
  title =        "{NIST Digital Library of Mathematical Functions}",
  journal =      j-ANN-MATH-ARTIF-INTELL,
  volume =       "38",
  number =       "1--3",
  pages =        "105--119",
  month =        may,
  year =         "2003",
  CODEN =        "AMAIEC",
  ISSN =         "1012-2443 (print), 1573-7470 (electronic)",
  ISSN-L =       "1012-2443",
  bibdate =      "Fri Jul 09 06:23:08 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/Linz01.ps",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematics and Artificial Intelligence",
  journal-URL =  "http://link.springer.com/journal/10472",
}


bibtype: inproceedings
filename: elefunt.bib
label: Markstein:2003:FQP
author: Peter Markstein
title: A fast quad precision elementary function library for Itanium
crossref: Anonymous:2003:CRN
pages: 5--12
year: 2003
bibdate: Fri Jun 24 20:14:39 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.06.24 20:14:39 ???
acknowledgement: ack-nhfb
rawauthor: Peter Markstein
rawtitle: A fast quad precision elementary function library for {Itanium}
abstract:
This talk will describe Itanium's floating point architecture and how it has been used to produce a high performance, highly accurate quad precision elementary function library.par Itanium's floating-point features will first be described, from the point of view of a computer architect. Many conflicting requirements vie for consideration during the design of a new computer architecture. These include instruction word size, number of registers, the set of operations, arithmetic precisions supported, and memory access. Some of the trade-offs during the design phase will be discussed.par One of the objectives of the original Itanium design was to accelerate quad precision arithmetic. The talk will describe how the Itanium elementary function library was constructed, with attention to performance and accuracy. Because a pair of double-extended floating point words are used for internal operations involving quad precision numbers, intermediate results, holding 128 bits, provide 15 guard bits during intermediate calculations, resulting in a very low percentage of misrounded results.

rawabstract:
This talk will describe Itanium's floating point architecture and how it has been used to produce a high performance, highly accurate quad precision elementary function library.\par Itanium's floating-point features will first be described, from the point of view of a computer architect. Many conflicting requirements vie for consideration during the design of a new computer architecture. These include instruction word size, number of registers, the set of operations, arithmetic precisions supported, and memory access. Some of the trade-offs during the design phase will be discussed.\par One of the objectives of the original Itanium design was to accelerate quad precision arithmetic. The talk will describe how the Itanium elementary function library was constructed, with attention to performance and accuracy. Because a pair of double-extended floating point words are used for internal operations involving quad precision numbers, intermediate results, holding 128 bits, provide 15 guard bits during intermediate calculations, resulting in a very low percentage of misrounded results.

entry:
@InProceedings{Markstein:2003:FQP,
  author =       "Peter Markstein",
  title =        "A fast quad precision elementary function library for
                 {Itanium}",
  crossref =     "Anonymous:2003:CRN",
  pages =        "5--12",
  year =         "2003",
  bibdate =      "Fri Jun 24 20:14:39 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This talk will describe Itanium's floating point
                 architecture and how it has been used to produce a high
                 performance, highly accurate quad precision elementary
                 function library.\par

                 Itanium's floating-point features will first be
                 described, from the point of view of a computer
                 architect. Many conflicting requirements vie for
                 consideration during the design of a new computer
                 architecture. These include instruction word size,
                 number of registers, the set of operations, arithmetic
                 precisions supported, and memory access. Some of the
                 trade-offs during the design phase will be
                 discussed.\par

                 One of the objectives of the original Itanium design
                 was to accelerate quad precision arithmetic. The talk
                 will describe how the Itanium elementary function
                 library was constructed, with attention to performance
                 and accuracy. Because a pair of double-extended
                 floating point words are used for internal operations
                 involving quad precision numbers, intermediate results,
                 holding 128 bits, provide 15 guard bits during
                 intermediate calculations, resulting in a very low
                 percentage of misrounded results.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Mason:2003:CP
author: J. C. Mason and D. C. Handscomb
title: Chebyshev Polynomials
publisher: pub-CHAPMAN-HALL-CRC
address: pub-CHAPMAN-HALL-CRC:adr
pages: xiii + 341
year: 2003
ISBN: 0-8493-0355-9 OR 0849303559
ISBN13: 978-0-8493-0355-5 OR 9780849303555
LCCN: QA404.5 .M37 2003
bibdate: Fri Apr 17 09:45:35 MDT 2009
bibtimestamp: 2009.04.17 09:45:35 MDT
subject: Chebyshev polynomials
acknowledgement: ack-nhfb
rawauthor: J. C. Mason and D. C. Handscomb
rawtitle: {Chebyshev} Polynomials
bibsource:
http://www.math.utah.edu/pub/tex/bib/mathcw.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager

entry:
@Book{Mason:2003:CP,
  author =       "J. C. Mason and D. C. Handscomb",
  title =        "{Chebyshev} Polynomials",
  publisher =    pub-CHAPMAN-HALL-CRC,
  address =      pub-CHAPMAN-HALL-CRC:adr,
  pages =        "xiii + 341",
  year =         "2003",
  ISBN =         "0-8493-0355-9",
  ISBN-13 =      "978-0-8493-0355-5",
  LCCN =         "QA404.5 .M37 2003",
  bibdate =      "Fri Apr 17 09:45:35 MDT 2009",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Chebyshev polynomials",
  xxauthor =     "J. C. Mason and D. C. (David Christopher) Handscomb",
  xxURL =        "http://www.loc.gov/catdir/enhancements/fy0646/2002073578-d.html",
}


bibtype: inproceedings
filename: elefunt.bib
label: Meunier:2003:EAG
author: Ludovic Meunier and Bruno Salvy
editor: Hoon Hong
title: ESF: an automatically generated encyclopedia of special functions
publisher: pub-ACM
address: pub-ACM:adr
pages: xiii + 341
month: aug
monthnumber: 8
year: 2003
DOI: https://doi.org/10.1145/860854.860898
ISBN: 1-58113-641-2 (paperback) OR 1581136412 (paperback)
ISBN13: 978-1-58113-641-8 (paperback) OR 9781581136418 (paperback)
LCCN: QA76.5 S98 2003; QA76.95.I59 2003
bibdate: Sat Nov 11 06:21:45 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.11.11 06:21:45 ???
acknowledgement: ack-nhfb
bookDOI: https://doi.org/10.1145/860854
bookURL: https://dl.acm.org/doi/proceedings/10.1145/860854
rawauthor: Ludovic Meunier and Bruno Salvy
raweditor: Hoon Hong
rawtitle: {ESF}: an automatically generated encyclopedia of special functions
booktitle:
Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation: Philadelphia, PA, USA, August 3--6, 2003

abstract:
We present our on-going work on the automatic generation of an encyclopedia of special functions on the web, called The Encyclopedia of Special Functions (ESF) (url http://algo.inria.fr/esf). All mathematical formulae in the ESF are computed, typeset and displayed without any human intervention. This is achieved by exploiting a collection of computer algebra algorithms in a systematic way, on top of a specially designed data structure for a class of special functions.

rawabstract:
We present our on-going work on the automatic generation of an encyclopedia of special functions on the web, called The Encyclopedia of Special Functions (ESF) (\url{http://algo.inria.fr/esf}). All mathematical formulae in the ESF are computed, typeset and displayed without any human intervention. This is achieved by exploiting a collection of computer algebra algorithms in a systematic way, on top of a specially designed data structure for a class of special functions.

rawbooktitle:
Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation: {Philadelphia, PA, USA, August 3--6, 2003}

entry:
@InProceedings{Meunier:2003:EAG,
  author =       "Ludovic Meunier and Bruno Salvy",
  editor =       "Hoon Hong",
  booktitle =    "Proceedings of the 2003 International Symposium on
                 Symbolic and Algebraic Computation: {Philadelphia, PA,
                 USA, August 3--6, 2003}",
  title =        "{ESF}: an automatically generated encyclopedia of
                 special functions",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  month =        aug,
  year =         "2003",
  DOI =          "https://doi.org/10.1145/860854.860898",
  ISBN =         "1-58113-641-2 (paperback)",
  ISBN-13 =      "978-1-58113-641-8 (paperback)",
  LCCN =         "QA76.5 S98 2003; QA76.95.I59 2003",
  bibdate =      "Sat Nov 11 06:21:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "We present our on-going work on the automatic
                 generation of an encyclopedia of special functions on
                 the web, called The Encyclopedia of Special Functions
                 (ESF) (\url{http://algo.inria.fr/esf}). All
                 mathematical formulae in the ESF are computed, typeset
                 and displayed without any human intervention. This is
                 achieved by exploiting a collection of computer algebra
                 algorithms in a systematic way, on top of a specially
                 designed data structure for a class of special
                 functions.",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1145/860854",
  book-URL =     "https://dl.acm.org/doi/proceedings/10.1145/860854",
}


bibtype: article
filename: elefunt.bib
label: Ovtchinnikov:2003:CEGb
author: E. Ovtchinnikov
journal: j-SIAM-J-NUMER-ANAL
volume: 41
number: 1
pages: 272--286
month: feb
monthnumber: 2
year: 2003
CODEN: SJNAAM
DOI: https://doi.org/10.1137/S0036142902411768
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
bibdate: Fri Aug 15 05:57:09 MDT 2003
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SINUM/41/1; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2003.08.15 05:57:09 MDT
URL: http://epubs.siam.org/sam-bin/dbq/article/41176
fjournal: SIAM Journal on Numerical Analysis
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: E. Ovtchinnikov
title:
Convergence Estimates for the Generalized Davidson Method for Symmetric Eigenvalue Problems II: The Subspace Acceleration

rawtitle:
Convergence Estimates for the Generalized {Davidson} Method for Symmetric Eigenvalue Problems {II}: The Subspace Acceleration

entry:
@Article{Ovtchinnikov:2003:CEGb,
  author =       "E. Ovtchinnikov",
  title =        "Convergence Estimates for the Generalized {Davidson}
                 Method for Symmetric Eigenvalue Problems {II}: The
                 Subspace Acceleration",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "41",
  number =       "1",
  pages =        "272--286",
  month =        feb,
  year =         "2003",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/S0036142902411768",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "Fri Aug 15 05:57:09 MDT 2003",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SINUM/41/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/41176",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Paris:2003:AEG
author: R. B. Paris
title: The asymptotic expansion of a generalised incomplete gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 151
number: 2
pages: 297--306
day: 15
month: feb
monthnumber: 2
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:33 MST 2017
bibtimestamp: 2017.02.25 12:52:33 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702008099
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: R. B. Paris
rawtitle: The asymptotic expansion of a generalised incomplete gamma function
entry:
@Article{Paris:2003:AEG,
  author =       "R. B. Paris",
  title =        "The asymptotic expansion of a generalised incomplete
                 gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "151",
  number =       "2",
  pages =        "297--306",
  day =          "15",
  month =        feb,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:33 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/S0377042702008099",
  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: Paszkowski:2003:CAS
author: Stefan Paszkowski
title: Convergence Acceleration of Some Continued Fractions
journal: j-NUMER-ALGORITHMS
volume: 32
number: 2--4
pages: 193--247
month: apr
monthnumber: 4
year: 2003
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Sep 29 08:37:11 MDT 2003
bibsource: http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2003.09.29 08:37:11 MDT
fjournal: Numerical Algorithms
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Stefan Paszkowski
rawtitle: Convergence Acceleration of Some Continued Fractions
URL:
http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/fulltext.pdf

entry:
@Article{Paszkowski:2003:CAS,
  author =       "Stefan Paszkowski",
  title =        "Convergence Acceleration of Some Continued Fractions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "32",
  number =       "2--4",
  pages =        "193--247",
  month =        apr,
  year =         "2003",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Sep 29 08:37:11 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Pedersen:2003:DGF
author: Henrik L. Pedersen
title: The double gamma function and related Pick functions
journal: j-J-COMPUT-APPL-MATH
volume: 153
number: 1--2
pages: 361--369
day: 1
month: apr
monthnumber: 4
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:34 MST 2017
bibtimestamp: 2017.02.25 12:52:34 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702006040
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Henrik L. Pedersen
rawtitle: The double gamma function and related {Pick} functions
entry:
@Article{Pedersen:2003:DGF,
  author =       "Henrik L. Pedersen",
  title =        "The double gamma function and related {Pick}
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "153",
  number =       "1--2",
  pages =        "361--369",
  day =          "1",
  month =        apr,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:34 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/S0377042702006040",
  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: Petropoulou:2003:CZB
author: Eugenia N. Petropoulou and Panayiotis D. Siafarikas and Ioannis D. Stabolas
title: On the common zeros of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 153
number: 1--2
pages: 387--393
day: 1
month: apr
monthnumber: 4
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:34 MST 2017
bibtimestamp: 2017.02.25 12:52:34 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702006416
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Eugenia N. Petropoulou and Panayiotis D. Siafarikas and Ioannis D. Stabolas
rawtitle: On the common zeros of {Bessel} functions
entry:
@Article{Petropoulou:2003:CZB,
  author =       "Eugenia N. Petropoulou and Panayiotis D. Siafarikas
                 and Ioannis D. Stabolas",
  title =        "On the common zeros of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "153",
  number =       "1--2",
  pages =        "387--393",
  day =          "1",
  month =        apr,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:34 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/S0377042702006416",
  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: Pineiro:2003:LHR
author: J.-A. Pineiro and J. D. Bruguera and M. D. Ercegovac
booktitle: ISCAS '03. Proceedings of the 2003 International Symposium on Circuits and Systems. 25--28 May 2003
title: On-line high-radix exponential with selection by rounding
volume: 4
publisher: pub-IEEE
address: pub-IEEE:adr
pages: IV-121--IV-124
year: 2003
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: J.-A. Pineiro and J. D. Bruguera and M. D. Ercegovac
rawtitle: On-line high-radix exponential with selection by rounding
rawbooktitle:
{ISCAS '03. Proceedings of the 2003 International Symposium on Circuits and Systems. 25--28 May 2003}

entry:
@InProceedings{Pineiro:2003:LHR,
  author =       "J.-A. Pineiro and J. D. Bruguera and M. D. Ercegovac",
  booktitle =    "{ISCAS '03. Proceedings of the 2003 International
                 Symposium on Circuits and Systems. 25--28 May 2003}",
  title =        "On-line high-radix exponential with selection by
                 rounding",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "IV-121--IV-124",
  year =         "2003",
  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 =      "An on-line high-radix algorithm for computing the
                 exponential function (e/sup x/) with arbitrary
                 precision n is presented. Selection by rounding and a
                 redundant digit-set for the digits e/sub j/ are used,
                 with selection by table in the first \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Sidi:2003:PEM
author: Avram Sidi
title: Practical Extrapolation Methods: Theory and Applications
volume: 10
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: xxii + 519
year: 2003
ISBN: 0-521-66159-5 OR 0521661595
ISBN13: 978-0-521-66159-1 OR 9780521661591
LCCN: QA281 .S555 2003
bibdate: Mon Jul 5 16:49:09 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.07.05 16:49:09 MDT
series: Cambridge monographs on applied and computational mathematics
subject: extrapolation
acknowledgement: ack-nhfb
rawauthor: Avram Sidi
rawtitle: Practical Extrapolation Methods: Theory and Applications
entry:
@Book{Sidi:2003:PEM,
  author =       "Avram Sidi",
  title =        "Practical Extrapolation Methods: Theory and
                 Applications",
  volume =       "10",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xxii + 519",
  year =         "2003",
  ISBN =         "0-521-66159-5",
  ISBN-13 =      "978-0-521-66159-1",
  LCCN =         "QA281 .S555 2003",
  bibdate =      "Mon Jul 5 16:49:09 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Cambridge monographs on applied and computational
                 mathematics",
  acknowledgement = ack-nhfb,
  subject =      "extrapolation",
  xxURL =        "http://www.loc.gov/catdir/samples/cam033/2002024669.html;
                 http://www.loc.gov/catdir/description/cam022/2002024669.html;
                 http://www.loc.gov/catdir/toc/cam024/2002024669.html",
}


bibtype: misc
filename: elefunt.bib
label: Tkachev:2003:EFI
author: Vladimir G. Tkachev
title: Elliptic functions: Introduction course
pages: xxii + 519
day: 25
month: nov
monthnumber: 11
year: 2003
bibdate: Wed Mar 15 08:43:21 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.15 08:43:21 ???
URL: http://users.mai.liu.se/vlatk48/teaching/lect2-agm.pdf
acknowledgement: ack-nhfb
howpublished: Web lecture notes.
rawauthor: Vladimir G. Tkachev
rawtitle: Elliptic functions: Introduction course
TOC:
Chapter 1. Elliptic integrals and Jacobi's theta functions / 5 1.1. Elliptic integrals and the AGM: real case / 5 1.1.3. The arithmetic-geometric mean iteration / 7 1.2. Lemniscates and elastic curves / 11 1.3. Euler's addition theorem / 18 1.4. Theta functions: preliminaries 5 / 24 Chapter 2. General theory of doubly periodic functions / 31 2.1. Preliminaries / 31 2.2. Periods of analytic functions / 33 2.3. Existence of doubly periodic functions / 36 2.4. Liouville's theorems / 38 2.5. The Weierstrass function $wp (z)$ / 43 2.6. Modular forms / 51 Bibliography / 61

rawTOC:
Chapter 1. Elliptic integrals and Jacobi's theta functions / 5 \\ 1.1. Elliptic integrals and the AGM: real case / 5 \\ 1.1.3. The arithmetic-geometric mean iteration / 7 \\ 1.2. Lemniscates and elastic curves / 11 \\ 1.3. Euler's addition theorem / 18 \\ 1.4. Theta functions: preliminaries 5 / 24 \\ Chapter 2. General theory of doubly periodic functions / 31 \\ 2.1. Preliminaries / 31 \\ 2.2. Periods of analytic functions / 33 \\ 2.3. Existence of doubly periodic functions / 36 \\ 2.4. Liouville's theorems / 38 \\ 2.5. The Weierstrass function $\wp(z)$ / 43 \\ 2.6. Modular forms / 51 \\ Bibliography / 61

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


bibtype: inproceedings
filename: elefunt.bib
label: Wang:2003:TDF
author: Xiaojun Wang and B. E. Nelson
title: Tradeoffs of designing floating-point division and square root on Virtex FPGAs
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 195--203
year: 2003
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: Xiaojun Wang and B. E. Nelson
rawtitle: Tradeoffs of designing floating-point division and square root on {Virtex FPGAs}
booktitle:
FCCM 2003: 11th Annual IEEE Symposium on Field-Programmable Custom Computing Machines, 9--11 April 2003

rawbooktitle:
{FCCM 2003}: 11th Annual {IEEE} Symposium on Field-Programmable Custom Computing Machines, 9--11 April 2003

entry:
@InProceedings{Wang:2003:TDF,
  author =       "Xiaojun Wang and B. E. Nelson",
  booktitle =    "{FCCM 2003}: 11th Annual {IEEE} Symposium on
                 Field-Programmable Custom Computing Machines, 9--11
                 April 2003",
  title =        "Tradeoffs of designing floating-point division and
                 square root on {Virtex FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "195--203",
  year =         "2003",
  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 =      "Low latency, high throughput and small area are three
                 major design considerations of an FPGA (field
                 programmable gate array) design. In this paper, we
                 present a high radix SRT division algorithm and a
                 binary restoring square root algorithm. We \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Yousif:2003:CBF
author: Hashim A. Yousif and Richard Melka
title: Computing Bessel functions of the second kind in extreme parameter regimes
journal: j-COMP-PHYS-COMM
volume: 151
number: 1
pages: 25--34
day: 1
month: mar
monthnumber: 3
year: 2003
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(02)00697-5
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 23:41:27 MST 2012
bibtimestamp: 2012.02.13 23:41:27 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465502006975
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Hashim A. Yousif and Richard Melka
rawtitle: Computing {Bessel} functions of the second kind in extreme parameter regimes
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathematica.bib

abstract:
A useful method of computing the integral order Bessel functions of the second kind $ Y_n(x + i y) $ 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 for extreme parameter regimes when $ x sim 0 $ (or $ y sim 0 $ ) and is useful because a number existing algorithms and methods fail to give correct results for small $x$ or small $y$. The approximating equations are derived by expanding the Bessel function in Taylor series, are tested and discussed. The present work is a continuation of the previous one conducted in regard to the Bessel function of the first kind. The results of our formalism are compared to the available existing numerical methods used in Mathematica, IMSL, MATLAB, and the Amos library. Our numerical method is easy to implement, efficient, and produces reliable results. In addition, this method reduces the computation of the Bessel functions of the second complex argument to that of real argument which simplify the computation considerably.

rawabstract:
A useful method of computing the integral order Bessel functions of the second kind $ Y_n(x + i y) $ 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 for extreme parameter regimes when $ x \sim 0 $ (or $ y \sim 0 $ ) and is useful because a number existing algorithms and methods fail to give correct results for small $x$ or small $y$. The approximating equations are derived by expanding the Bessel function in Taylor series, are tested and discussed. The present work is a continuation of the previous one conducted in regard to the Bessel function of the first kind. The results of our formalism are compared to the available existing numerical methods used in Mathematica, IMSL, MATLAB, and the Amos library. Our numerical method is easy to implement, efficient, and produces reliable results. In addition, this method reduces the computation of the Bessel functions of the second complex argument to that of real argument which simplify the computation considerably.

entry:
@Article{Yousif:2003:CBF,
  author =       "Hashim A. Yousif and Richard Melka",
  title =        "Computing {Bessel} functions of the second kind in
                 extreme parameter regimes",
  journal =      j-COMP-PHYS-COMM,
  volume =       "151",
  number =       "1",
  pages =        "25--34",
  day =          "1",
  month =        mar,
  year =         "2003",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(02)00697-5",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 23:41:27 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465502006975",
  abstract =     "A useful method of computing the integral order Bessel
                 functions of the second kind $ Y_n(x + i y) $ 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 for extreme parameter regimes when
                 $ x \sim 0 $ (or $ y \sim 0 $ ) and is useful because a
                 number existing algorithms and methods fail to give
                 correct results for small $x$ or small $y$. The
                 approximating equations are derived by expanding the
                 Bessel function in Taylor series, are tested and
                 discussed. The present work is a continuation of the
                 previous one conducted in regard to the Bessel function
                 of the first kind. The results of our formalism are
                 compared to the available existing numerical methods
                 used in Mathematica, IMSL, MATLAB, and the Amos
                 library. Our numerical method is easy to implement,
                 efficient, and produces reliable results. In addition,
                 this method reduces the computation of the Bessel
                 functions of the second complex argument to that of
                 real argument which simplify the computation
                 considerably.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: book
filename: elefunt.bib
label: Zwillinger:2003:CSM
editor: Daniel Zwillinger
title: CRC Standard Mathematical Tables and Formulae
publisher: pub-CHAPMAN-HALL-CRC
address: pub-CHAPMAN-HALL-CRC:adr
edition: 31st
pages: xiv + 910
year: 2003
ISBN: 1-58488-291-3, 1-4200-3534-7 (electronic) OR 1584882913, 1420035347 (electronic)
ISBN13: 978-1-58488-291-6, 978-1-4200-3534-6 (electronic) OR 9781584882916, 9781420035346 (electronic)
LCCN: QA47 .M315 2003
bibdate: Thu Nov 25 11:07:20 MST 2010
bibtimestamp: 2010.11.25 11:07:20 MST
subject: mathematics; tables
acknowledgement: ack-nhfb
raweditor: Daniel Zwillinger
rawtitle: {CRC} Standard Mathematical Tables and Formulae
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/mathcw.bib; prodorbis.library.yale.edu:7090/voyager

entry:
@Book{Zwillinger:2003:CSM,
  editor =       "Daniel Zwillinger",
  title =        "{CRC} Standard Mathematical Tables and Formulae",
  publisher =    pub-CHAPMAN-HALL-CRC,
  address =      pub-CHAPMAN-HALL-CRC:adr,
  edition =      "31st",
  pages =        "xiv + 910",
  year =         "2003",
  ISBN =         "1-58488-291-3, 1-4200-3534-7 (electronic)",
  ISBN-13 =      "978-1-58488-291-6, 978-1-4200-3534-6 (electronic)",
  LCCN =         "QA47 .M315 2003",
  bibdate =      "Thu Nov 25 11:07:20 MST 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  acknowledgement = ack-nhfb,
  subject =      "mathematics; tables",
}


bibtype: book
filename: elefunt.bib
label: Bell:2004:SFS
author: W. W. (William Wallace) Bell
title: Special functions for scientists and engineers
publisher: pub-DOVER
address: pub-DOVER:adr
pages: xiv + 247
year: 2004
ISBN: 0-486-43521-0 OR 0486435210
ISBN13: 978-0-486-43521-3 OR 9780486435213
LCCN: QA351 .B4 2004
bibdate: Sat Oct 30 16:30:44 MDT 2010
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 16:30:44 MDT
series: Dover books on mathematics
remark: Reprinting of cite Bell:1968:SFS.
subject: Functions, Special
acknowledgement: ack-nhfb
rawauthor: W. W. (William Wallace) Bell
rawtitle: Special functions for scientists and engineers
entry:
@Book{Bell:2004:SFS,
  author =       "W. W. (William Wallace) Bell",
  title =        "Special functions for scientists and engineers",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xiv + 247",
  year =         "2004",
  ISBN =         "0-486-43521-0",
  ISBN-13 =      "978-0-486-43521-3",
  LCCN =         "QA351 .B4 2004",
  bibdate =      "Sat Oct 30 16:30:44 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Dover books on mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Reprinting of \cite{Bell:1968:SFS}.",
  subject =      "Functions, Special",
}


bibtype: article
filename: elefunt.bib
label: Berrut:2004:APS
author: Jean-Paul Berrut and Hans D. Mittelmann
title: Adaptive Point Shifts in Rational Approximation with Optimized Denominator
journal: j-J-COMPUT-APPL-MATH
volume: 164--165
pages: 81--92
day: 1
month: mar
monthnumber: 3
year: 2004
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(03)00485-0
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Tue Mar 24 21:10:48 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2009.03.24 21:10:48 ???
fjournal: Journal of Computational and Applied Mathematics
keywords: interpolation; optimal interpolation; point shifts; rational approximation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Jean-Paul Berrut and Hans D. Mittelmann
rawtitle: Adaptive Point Shifts in Rational Approximation with Optimized Denominator
note:
Proceedings of the 10th International Congress on Computational and Applied Mathematics University of Leuven, Belgium, 22--26 July 2002. Edited by M. J. Goovaerts, S. Vandewalle, and L. Wuytack.

abstract:
Classical rational interpolation is known to suffer from several drawbacks, such as unattainable points and randomly located poles for a small number of nodes, as well as an erratic behavior of the error as this number grows larger. In a former article, we have suggested to obtain rational interpolants by a procedure that attaches optimally placed poles to the interpolating polynomial, using the barycentric representation of the interpolants. In order to improve upon the condition of the derivatives in the solution of differential equations, we have then experimented with a conformal point shift suggested by Kosloff and Tal-Ezer. As it turned out, such shifts can achieve a spectacular improvement in the quality of the approximation itself for functions with a large gradient in the center of the interval. This leads us to the present work which combines the pole attachment method with shifts optimally adjusted to the interpolated function. Such shifts are also constructed for functions with several shocks away from the extremities of the interval.

rawabstract:
Classical rational interpolation is known to suffer from several drawbacks, such as unattainable points and randomly located poles for a small number of nodes, as well as an erratic behavior of the error as this number grows larger. In a former article, we have suggested to obtain rational interpolants by a procedure that attaches optimally placed poles to the interpolating polynomial, using the barycentric representation of the interpolants. In order to improve upon the condition of the derivatives in the solution of differential equations, we have then experimented with a conformal point shift suggested by Kosloff and Tal-Ezer. As it turned out, such shifts can achieve a spectacular improvement in the quality of the approximation itself for functions with a large gradient in the center of the interval. This leads us to the present work which combines the pole attachment method with shifts optimally adjusted to the interpolated function. Such shifts are also constructed for functions with several shocks away from the extremities of the interval.

rawnote:
Proceedings of the 10th International Congress on Computational and Applied Mathematics University of Leuven, Belgium, 22--26 July 2002. Edited by M. J. Goovaerts, S. Vandewalle, and L. Wuytack.

entry:
@Article{Berrut:2004:APS,
  author =       "Jean-Paul Berrut and Hans D. Mittelmann",
  title =        "Adaptive Point Shifts in Rational Approximation with
                 Optimized Denominator",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "164--165",
  number =       "??",
  pages =        "81--92",
  day =          "1",
  month =        mar,
  year =         "2004",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(03)00485-0",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Tue Mar 24 21:10:48 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the 10th International Congress on
                 Computational and Applied Mathematics University of
                 Leuven, Belgium, 22--26 July 2002. Edited by M. J.
                 Goovaerts, S. Vandewalle, and L. Wuytack.",
  abstract =     "Classical rational interpolation is known to suffer
                 from several drawbacks, such as unattainable points and
                 randomly located poles for a small number of nodes, as
                 well as an erratic behavior of the error as this number
                 grows larger. In a former article, we have suggested to
                 obtain rational interpolants by a procedure that
                 attaches optimally placed poles to the interpolating
                 polynomial, using the barycentric representation of the
                 interpolants. In order to improve upon the condition of
                 the derivatives in the solution of differential
                 equations, we have then experimented with a conformal
                 point shift suggested by Kosloff and Tal-Ezer. As it
                 turned out, such shifts can achieve a spectacular
                 improvement in the quality of the approximation itself
                 for functions with a large gradient in the center of
                 the interval. This leads us to the present work which
                 combines the pole attachment method with shifts
                 optimally adjusted to the interpolated function. Such
                 shifts are also constructed for functions with several
                 shocks away from the extremities of the interval.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "interpolation; optimal interpolation; point shifts;
                 rational approximation",
}


bibtype: incollection
filename: elefunt.bib
label: Borwein:2004:AGMa
author: J. M. Borwein and P. B. Borwein
title: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
crossref: Berggren:2004:PSB
pages: 537--552
year: 2004
DOI: https://doi.org/10.1007/978-1-4757-4217-6_56
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibtimestamp: 2016.08.11 09:36:22 MDT
note: Reprint of cite Borwein:1984:AGM.
URL: http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_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:2004:AGMa,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:2004:PSB",
  pages =        "537--552",
  year =         "2004",
  DOI =          "https://doi.org/10.1007/978-1-4757-4217-6_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Borwein:1984:AGM}.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_56",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: elefunt.bib
label: Brisebarre:2004:ACR
author: N. Brisebarre and J.-M. Muller and Saurabh Kumar Raina
title: Accelerating correctly rounded floating-point division when the divisor is known in advance
journal: j-IEEE-TRANS-COMPUT
volume: 53
number: 8
pages: 1069--1072
month: aug
monthnumber: 8
year: 2004
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2004.37
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
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 Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. Brisebarre and J.-M. Muller and Saurabh Kumar Raina
rawtitle: Accelerating correctly rounded floating-point division when the divisor is known in advance
abstract:
We present techniques for accelerating the floating-point computation of $ x / y $ when $y$ is known before $x$. The proposed algorithms are oriented toward architectures with available fused-mac operations. The goal is to get exactly the same result as with ldots 

rawabstract:
We present techniques for accelerating the floating-point computation of $ x / y $ when $y$ is known before $x$. The proposed algorithms are oriented toward architectures with available fused-mac operations. The goal is to get exactly the same result as with \ldots{}

entry:
@Article{Brisebarre:2004:ACR,
  author =       "N. Brisebarre and J.-M. Muller and Saurabh Kumar
                 Raina",
  title =        "Accelerating correctly rounded floating-point division
                 when the divisor is known in advance",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "8",
  pages =        "1069--1072",
  month =        aug,
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.37",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "We present techniques for accelerating the
                 floating-point computation of $ x / y $ when $y$ is
                 known before $x$. The proposed algorithms are oriented
                 toward architectures with available fused-mac
                 operations. The goal is to get exactly the same result
                 as with \ldots{}",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "We present techniques for accelerating the
                 floating-point computation of x/y when y is known
                 before x. The proposed algorithms are oriented toward
                 architectures with available fused-mac operations. The
                 goal is to get exactly the same result as with
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Chaudhry:2004:EHC
author: M. Aslam Chaudhry and Asghar Qadir and H. M. Srivastava and R. B. Paris
title: Extended hypergeometric and confluent hypergeometric functions
journal: j-APPL-MATH-COMP
volume: 159
number: 2
pages: 589--602
day: 6
month: dec
monthnumber: 12
year: 2004
CODEN: AMHCBQ
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Mon Jul 4 09:15:38 MDT 2005
bibtimestamp: 2005.07.04 09:15:38 MDT
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: M. Aslam Chaudhry and Asghar Qadir and H. M. Srivastava and R. B. Paris
rawtitle: Extended hypergeometric and confluent hypergeometric functions
bibsource:
http://www.sciencedirect.com/science/journal/00963003; https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Chaudhry:2004:EHC,
  author =       "M. Aslam Chaudhry and Asghar Qadir and H. M.
                 Srivastava and R. B. Paris",
  title =        "Extended hypergeometric and confluent hypergeometric
                 functions",
  journal =      j-APPL-MATH-COMP,
  volume =       "159",
  number =       "2",
  pages =        "589--602",
  day =          "6",
  month =        dec,
  year =         "2004",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon Jul 4 09:15:38 MDT 2005",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: Croot:2004:ACC
author: Ernie Croot and Ren-Cang Li and H. J. Hui June Zhu
title: The em abc conjecture and correctly rounded reciprocal square roots
journal: j-THEOR-COMP-SCI
volume: 315
number: 2--3
pages: 405--417
day: 6
month: may
monthnumber: 5
year: 2004
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Thu Nov 4 10:19:15 MST 2004
bibtimestamp: 2004.11.04 10:19:15 MST
fjournal: Theoretical Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03043975
rawauthor: Ernie Croot and Ren-Cang Li and H. J. Hui June Zhu
rawtitle: The {\em abc\/} conjecture and correctly rounded reciprocal square roots
bibsource:
http://www.sciencedirect.com/science/journal/03043975; 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/tcs2000.bib

abstract:
The reciprocal square root calculation $ alpha = 1 / sqrt x $ is very common in scientific computations. Having a correctly rounded implementation of it is of great importance in producing numerically predictable code among today's heterogeneous computing environment. Existing results suggest that to get the correctly rounded $ alpha $ in a floating point number system with $p$ significant bits, we may have to compute up to $ 3 p + 1 $ leading bits of $ alpha $. However, numerical evidence indicates the actual number may be as small as $ 2 p $ plus a few more bits. This paper attempts to bridge the gap by showing that this is indeed true, assuming the em abc conjecture which is widely purported to hold. (But our results do not tell exactly how many more bits beyond the $ 2 p $ bits, due to the fact that the constants involved in the conjecture are ineffective.) Along the way, rough bounds which are comparable to the existing ones are also proven. The technique used here is a combination of the classical Liouville's estimation and contemporary number theory.

rawabstract:
The reciprocal square root calculation $ \alpha = 1 / \sqrt {x} $ is very common in scientific computations. Having a correctly rounded implementation of it is of great importance in producing numerically predictable code among today's heterogeneous computing environment. Existing results suggest that to get the correctly rounded $ \alpha $ in a floating point number system with $p$ significant bits, we may have to compute up to $ 3 p + 1 $ leading bits of $ \alpha $. However, numerical evidence indicates the actual number may be as small as $ 2 p $ plus a few more bits. This paper attempts to bridge the gap by showing that this is indeed true, assuming the {\em abc\/} conjecture which is widely purported to hold. (But our results do not tell exactly how many more bits beyond the $ 2 p $ bits, due to the fact that the constants involved in the conjecture are ineffective.) Along the way, rough bounds which are comparable to the existing ones are also proven. The technique used here is a combination of the classical Liouville's estimation and contemporary number theory.

entry:
@Article{Croot:2004:ACC,
  author =       "Ernie Croot and Ren-Cang Li and H. J. Hui June Zhu",
  title =        "The {\em abc\/} conjecture and correctly rounded
                 reciprocal square roots",
  journal =      j-THEOR-COMP-SCI,
  volume =       "315",
  number =       "2--3",
  pages =        "405--417",
  day =          "6",
  month =        may,
  year =         "2004",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Thu Nov 4 10:19:15 MST 2004",
  bibsource =    "http://www.sciencedirect.com/science/journal/03043975;
                 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/tcs2000.bib",
  abstract =     "The reciprocal square root calculation $ \alpha = 1 /
                 \sqrt {x} $ is very common in scientific computations.
                 Having a correctly rounded implementation of it is of
                 great importance in producing numerically predictable
                 code among today's heterogeneous computing environment.
                 Existing results suggest that to get the correctly
                 rounded $ \alpha $ in a floating point number system
                 with $p$ significant bits, we may have to compute up to
                 $ 3 p + 1 $ leading bits of $ \alpha $. However,
                 numerical evidence indicates the actual number may be
                 as small as $ 2 p $ plus a few more bits. This paper
                 attempts to bridge the gap by showing that this is
                 indeed true, assuming the {\em abc\/} conjecture which
                 is widely purported to hold. (But our results do not
                 tell exactly how many more bits beyond the $ 2 p $
                 bits, due to the fact that the constants involved in
                 the conjecture are ineffective.) Along the way, rough
                 bounds which are comparable to the existing ones are
                 also proven. The technique used here is a combination
                 of the classical Liouville's estimation and
                 contemporary number theory.",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}


bibtype: inproceedings
filename: elefunt.bib
label: deDinechin:2004:PCR
author: Florent de Dinechin and Catherine Loirat and Jean-Michel Muller
title: A proven correctly rounded logarithm in double-precision
crossref: Frougny:2004:RCR
pages: 71--85
year: 2004
bibdate: Fri Nov 17 07:00:31 2023
bibtimestamp: 2023.11.17 07:00:31 ???
URL: http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_07_dinechin.pdf
keywords: arithmetic; correct rounding; elementary functions; floating-point; libm; logarithm
acknowledgement: ack-nhfb
rawauthor: Florent de Dinechin and Catherine Loirat and Jean-Michel Muller
rawtitle: A proven correctly rounded logarithm in double-precision
abstract:
This article is a case study in the implementation of a proven, portable, and efficient correctly rounded elementary function in double-precision. We describe the methodology used in the implementation of the natural logarithm in the crlibm library. The discipline required to prove a tight bound on the overall evaluation error allows to design a very efficient implementation with moderate effort.

rawabstract:
This article is a case study in the implementation of a proven, portable, and efficient correctly rounded elementary function in double-precision. We describe the methodology used in the implementation of the natural logarithm in the crlibm library. The discipline required to prove a tight bound on the overall evaluation error allows to design a very efficient implementation with moderate effort.

entry:
@InProceedings{deDinechin:2004:PCR,
  author =       "Florent de Dinechin and Catherine Loirat and
                 Jean-Michel Muller",
  title =        "A proven correctly rounded logarithm in
                 double-precision",
  crossref =     "Frougny:2004:RCR",
  pages =        "71--85",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_07_dinechin.pdf",
  abstract =     "This article is a case study in the implementation of
                 a proven, portable, and efficient correctly rounded
                 elementary function in double-precision. We describe
                 the methodology used in the implementation of the
                 natural logarithm in the crlibm library. The discipline
                 required to prove a tight bound on the overall
                 evaluation error allows to design a very efficient
                 implementation with moderate effort.",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic; correct rounding; elementary functions;
                 floating-point; libm; logarithm",
}


bibtype: article
filename: elefunt.bib
label: Defour:2004:PSM
title: Proposal for a Standardization of Mathematical Function Implementation in Floating-Point Arithmetic
journal: j-NUMER-ALGORITHMS
volume: 37
number: 1--4
pages: 367--375
month: dec
monthnumber: 12
year: 2004
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Dec 6 07:00:28 MST 2004
bibsource: http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.12.06 07:00:28 MST
fjournal: Numerical Algorithms
remark: Special Issue: SCAN'2002 International Conference (Guest Editors: Ren e Alt and Jean-Luc Lamotte)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawtitle: Proposal for a Standardization of Mathematical Function Implementation in Floating-Point Arithmetic
author:
David Defour and Guillaume Hanrot and Vincent Lefevre and Jean-Michel Muller and Nathalie Revol and Paul Zimmermann

URL:
http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/30/abstract.htm; http://perso.ens-lyon.fr/jean-michel.muller/NumAlg04.pdf; http://www.loria.fr/~zimmerma/papers/PropStandFunctions.pdf

rawauthor:
David Defour and Guillaume Hanrot and Vincent Lef{\`e}vre and Jean-Michel Muller and Nathalie Revol and Paul Zimmermann

entry:
@Article{Defour:2004:PSM,
  author =       "David Defour and Guillaume Hanrot and Vincent
                 Lef{\`e}vre and Jean-Michel Muller and Nathalie Revol
                 and Paul Zimmermann",
  title =        "Proposal for a Standardization of Mathematical
                 Function Implementation in Floating-Point Arithmetic",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "37",
  number =       "1--4",
  pages =        "367--375",
  month =        dec,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 6 07:00:28 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/30/abstract.htm;
                 http://perso.ens-lyon.fr/jean-michel.muller/NumAlg04.pdf;
                 http://www.loria.fr/~zimmerma/papers/PropStandFunctions.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  remark =       "Special Issue: SCAN'2002 International Conference
                 (Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)",
}


bibtype: inproceedings
filename: elefunt.bib
label: Doss:2004:FBI
author: C. C. Doss and R. L. Riley, Jr.
title: FPGA-based implementation of a robust IEEE-754 exponential unit
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 229--238
year: 2004
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: C. C. Doss and R. L. {Riley, Jr.}
rawtitle: {FPGA}-based implementation of a robust {IEEE-754} exponential unit
booktitle:
FCCM 2004. 12th Annual IEEE Symposium on Field-Programmable Custom Computing Machines, 20--23 April 2004

rawbooktitle:
{FCCM 2004}. 12th Annual {IEEE} Symposium on Field-Programmable Custom Computing Machines, 20--23 April 2004

entry:
@InProceedings{Doss:2004:FBI,
  author =       "C. C. Doss and R. L. {Riley, Jr.}",
  booktitle =    "{FCCM 2004}. 12th Annual {IEEE} Symposium on
                 Field-Programmable Custom Computing Machines, 20--23
                 April 2004",
  title =        "{FPGA}-based implementation of a robust {IEEE-754}
                 exponential unit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "229--238",
  year =         "2004",
  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 =      "This work explores the feasibility of implementing a
                 floating-point exponentiation unit on reconfigurable
                 computing systems. A table-driven exponentiation unit
                 was implemented using synthesizable VHDL. The project
                 included creating pipelined \ldots{}",
}


bibtype: techreport
filename: elefunt.bib
label: Ercegovac:2004:CSRa
author: Milos Ercegovac and Jean-Michel Muller
title: Complex Square Root with Operand Prescaling
type: Research Report
number: RR2004-42
institution: Ecole Normale Superieure de Lyon
address: 69364 Lyon Cedex 07, France
pages: 2 + 12
month: sep
monthnumber: 9
year: 2004
bibdate: Mon Dec 06 11:07:40 2004
bibtimestamp: 2004.12.06 11:07:40 ???
URL: http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-42.pdf
keywords: complex square-root; Computer arithmetic; digit-recurrence algorithm; operand prescaling.
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} Ercegovac and Jean-Michel Muller
rawtitle: Complex Square Root with Operand Prescaling
bibsource:
http://www.ens-lyon.fr/LIP/Pub/rr2004.php; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
We propose a radix-$r$ digit-recurrence algorithm for complex square-root. The operand is prescaled to allow the selection of square-root digits by rounding of the residual. This leads to a simple hardware implementation. Moreover, the use of digit recurrence approach allows correct rounding of the result. The algorithm, compatible with the complex division, and its design are described at a high-level. We also give rough comparisons of its latency and cost with respect to implementation based on standard floating-point instructions as used in software routines for complex square root.

rawabstract:
We propose a radix-$r$ digit-recurrence algorithm for complex square-root. The operand is prescaled to allow the selection of square-root digits by rounding of the residual. This leads to a simple hardware implementation. Moreover, the use of digit recurrence approach allows correct rounding of the result. The algorithm, compatible with the complex division, and its design are described at a high-level. We also give rough comparisons of its latency and cost with respect to implementation based on standard floating-point instructions as used in software routines for complex square root.

entry:
@TechReport{Ercegovac:2004:CSRa,
  author =       "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
  title =        "Complex Square Root with Operand Prescaling",
  type =         "Research Report",
  number =       "RR2004-42",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 12",
  month =        sep,
  year =         "2004",
  bibdate =      "Mon Dec 06 11:07:40 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-42.pdf",
  abstract =     "We propose a radix-$r$ digit-recurrence algorithm for
                 complex square-root. The operand is prescaled to allow
                 the selection of square-root digits by rounding of the
                 residual. This leads to a simple hardware
                 implementation. Moreover, the use of digit recurrence
                 approach allows correct rounding of the result. The
                 algorithm, compatible with the complex division, and
                 its design are described at a high-level. We also give
                 rough comparisons of its latency and cost with respect
                 to implementation based on standard floating-point
                 instructions as used in software routines for complex
                 square root.",
  acknowledgement = ack-nhfb,
  keywords =     "complex square-root; Computer arithmetic;
                 digit-recurrence algorithm; operand prescaling.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ercegovac:2004:CSRb
author: Milos Ercegovac and Jean-Michel Muller
title: Complex square root with operand prescaling
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 52--62
year: 2004
DOI: https://doi.org/10.1109/ASAP.2004.1342458
ISBN: 0-7695-2226-2 OR 0769522262
ISBN13: 978-0-7695-2226-5 OR 9780769522265
ISSN: 1063-6862 OR 10636862
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} Ercegovac and Jean-Michel Muller
rawtitle: Complex square root with operand prescaling
booktitle:
Proceedings of the 15th IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2004

rawbooktitle:
{Proceedings of the 15th IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2004}

entry:
@InProceedings{Ercegovac:2004:CSRb,
  author =       "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
  booktitle =    "{Proceedings of the 15th IEEE International Conference
                 on Application-Specific Systems, Architectures and
                 Processors, 2004}",
  title =        "Complex square root with operand prescaling",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "52--62",
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ASAP.2004.1342458",
  ISBN =         "0-7695-2226-2",
  ISBN-13 =      "978-0-7695-2226-5",
  ISSN =         "1063-6862",
  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",
  acknowledgement = ack-nhfb,
  summary =      "We propose a radix-r digit-recurrence algorithm for
                 complex square-root. The operand is prescaled to allow
                 the selection of square-root digits by rounding of the
                 residual. This leads to a simple hardware
                 implementation. Moreover, the use of digit \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Fabijonas:2004:AAF
author: B. R. Fabijonas
title: Algorithm 838: Airy Functions
journal: j-TOMS
volume: 30
number: 4
pages: 491--501
month: dec
monthnumber: 12
year: 2004
CODEN: ACMSCU
DOI: https://doi.org/10.1145/1039813.1039819
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Apr 12 06:34:31 MDT 2005
bibtimestamp: 2005.04.12 06:34:31 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: B. R. Fabijonas
rawtitle: {Algorithm 838}: {Airy} Functions
abstract:
We present a Fortran 90 module, which computes the solutions and their derivatives of Airy's differential equation, both on the real line and in the complex plane. The module also computes the zeros and associated values of the solutions and their derivatives, and the modulus and phase functions on the negative real axis. The computational methods are numerical integration of the differential equation and summation of asymptotic expansions for large argument. These methods were chosen because they are simple, adaptable to any precision, and amenable to rigorous error analysis. The module can be used to validate other codes or as a component in programs that require Airy functions.

rawabstract:
We present a Fortran 90 module, which computes the solutions and their derivatives of Airy's differential equation, both on the real line and in the complex plane. The module also computes the zeros and associated values of the solutions and their derivatives, and the modulus and phase functions on the negative real axis. The computational methods are numerical integration of the differential equation and summation of asymptotic expansions for large argument. These methods were chosen because they are simple, adaptable to any precision, and amenable to rigorous error analysis. The module can be used to validate other codes or as a component in programs that require Airy functions.

entry:
@Article{Fabijonas:2004:AAF,
  author =       "B. R. Fabijonas",
  title =        "{Algorithm 838}: {Airy} Functions",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "491--501",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1039813.1039819",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  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 =     "We present a Fortran 90 module, which computes the
                 solutions and their derivatives of Airy's differential
                 equation, both on the real line and in the complex
                 plane. The module also computes the zeros and
                 associated values of the solutions and their
                 derivatives, and the modulus and phase functions on the
                 negative real axis. The computational methods are
                 numerical integration of the differential equation and
                 summation of asymptotic expansions for large argument.
                 These methods were chosen because they are simple,
                 adaptable to any precision, and amenable to rigorous
                 error analysis. The module can be used to validate
                 other codes or as a component in programs that require
                 Airy functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Fabijonas:2004:CCA
author: B. R. Fabijonas and D. W. Lozier and F. W. J. Olver
journal: j-TOMS
volume: 30
number: 4
pages: 471--490
month: dec
monthnumber: 12
year: 2004
CODEN: ACMSCU
DOI: https://doi.org/10.1145/1039813.1039818
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Apr 12 06:34:31 MDT 2005
bibtimestamp: 2005.04.12 06:34:31 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: B. R. Fabijonas and D. W. Lozier and F. W. J. Olver
title:
Computation of complex Airy functions and their zeros using asymptotics and the differential equation

abstract:
We describe a method by which one can compute the solutions of Airy's differential equation, and their derivatives, both on the real line and in the complex plane. The computational methods are numerical integration of the differential equation and summation of asymptotic expansions for large argument. We give details involved in obtaining all of the parameter values, and we control the truncation errors rigorously. Using the same computational methods, we describe an algorithm that computes the zeros and associated values of the Airy functions and their derivatives, and the modulus and phase functions on the negative real axis.

rawabstract:
We describe a method by which one can compute the solutions of Airy's differential equation, and their derivatives, both on the real line and in the complex plane. The computational methods are numerical integration of the differential equation and summation of asymptotic expansions for large argument. We give details involved in obtaining all of the parameter values, and we control the truncation errors rigorously. Using the same computational methods, we describe an algorithm that computes the zeros and associated values of the Airy functions and their derivatives, and the modulus and phase functions on the negative real axis.

rawtitle:
Computation of complex {Airy} functions and their zeros using asymptotics and the differential equation

entry:
@Article{Fabijonas:2004:CCA,
  author =       "B. R. Fabijonas and D. W. Lozier and F. W. J. Olver",
  title =        "Computation of complex {Airy} functions and their
                 zeros using asymptotics and the differential equation",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "471--490",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1039813.1039818",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  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 =     "We describe a method by which one can compute the
                 solutions of Airy's differential equation, and their
                 derivatives, both on the real line and in the complex
                 plane. The computational methods are numerical
                 integration of the differential equation and summation
                 of asymptotic expansions for large argument. We give
                 details involved in obtaining all of the parameter
                 values, and we control the truncation errors
                 rigorously. Using the same computational methods, we
                 describe an algorithm that computes the zeros and
                 associated values of the Airy functions and their
                 derivatives, and the modulus and phase functions on the
                 negative real axis.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gebali:2004:EAF
author: Fayez Gebali and Mohamed Watheq El-Kharashi
title: ERL: an algorithm for fast evaluation of exponential, reciprocal, and logarithmic functions
crossref: Wahdan:2004:IHE
pages: 269--272
year: 2004
bibdate: Sat Jul 16 18:04:58 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 18:04:58 MDT
acknowledgement: ack-nhfb
rawauthor: Fayez Gebali and Mohamed Watheq El-Kharashi
rawtitle: {ERL}: an algorithm for fast evaluation of exponential, reciprocal, and logarithmic functions
abstract:
A fast algorithm (ERL) is proposed for evaluating Exponential, Reciprocal, and Logarithmic functions. The algorithm requires two to three iterations to complete using simple operations such as multiply, accumulate, and table lookup. The algorithm is independent of the number format used by the machine. Thus it can be implemented using the IEEE 754 floating-point standard or any other special format used by special-purpose processors. The dynamic range of the algorithm is limited only by the dynamic range of the machine on which it is implemented Numerical simulations are performed which verifies the speed and accuracy of the algorithm.

rawabstract:
A fast algorithm (ERL) is proposed for evaluating Exponential, Reciprocal, and Logarithmic functions. The algorithm requires two to three iterations to complete using simple operations such as multiply, accumulate, and table lookup. The algorithm is independent of the number format used by the machine. Thus it can be implemented using the IEEE 754 floating-point standard or any other special format used by special-purpose processors. The dynamic range of the algorithm is limited only by the dynamic range of the machine on which it is implemented Numerical simulations are performed which verifies the speed and accuracy of the algorithm.

entry:
@InProceedings{Gebali:2004:EAF,
  author =       "Fayez Gebali and Mohamed Watheq El-Kharashi",
  title =        "{ERL}: an algorithm for fast evaluation of
                 exponential, reciprocal, and logarithmic functions",
  crossref =     "Wahdan:2004:IHE",
  pages =        "269--272",
  year =         "2004",
  bibdate =      "Sat Jul 16 18:04:58 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A fast algorithm (ERL) is proposed for evaluating
                 Exponential, Reciprocal, and Logarithmic functions. The
                 algorithm requires two to three iterations to complete
                 using simple operations such as multiply, accumulate,
                 and table lookup. The algorithm is independent of the
                 number format used by the machine. Thus it can be
                 implemented using the IEEE 754 floating-point standard
                 or any other special format used by special-purpose
                 processors. The dynamic range of the algorithm is
                 limited only by the dynamic range of the machine on
                 which it is implemented Numerical simulations are
                 performed which verifies the speed and accuracy of the
                 algorithm.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Gil:2004:AMB
author: Amparo Gil and Javier Segura and Nico M. Temme
title: Algorithm 831: Modified Bessel functions of imaginary order and positive argument
journal: j-TOMS
volume: 30
number: 2
pages: 159--164
month: jun
monthnumber: 6
year: 2004
CODEN: ACMSCU
DOI: https://doi.org/10.1145/992200.992204
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Jun 10 07:24:58 MDT 2004
bibtimestamp: 2004.06.10 07:24:58 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
rawtitle: {Algorithm 831}: {Modified} {Bessel} functions of imaginary order and positive argument
abstract:
Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions $ K_ia(x) $, $ L_ia(x) $ and their derivatives for real $a$ and positive $x$; these functions are independent solutions of the differential equation $ x^2 w'' + x w' + (a^2 - x^2)w = 0 $. The code also computes exponentially scaled functions. The range of computation is $ (x, a) in (0, 1500] times [ - 1500, 1500] $ when scaled functions are considered and it is larger than $ (0, 500] times [ - 400, 400] $ for standard IEEE double precision arithmetic. The relative accuracy is better than $ 10^-13 $ in the range $ (0, 200] times [ - 200, 200] $ and close to $ 10^-12 $ in $ (0, 1500] times [ - 1500, 1500] $.

rawabstract:
Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions $ K_{ia}(x) $, $ L_{ia}(x) $ and their derivatives for real $a$ and positive $x$; these functions are independent solutions of the differential equation $ x^2 w'' + x w' + (a^2 - x^2)w = 0 $. The code also computes exponentially scaled functions. The range of computation is $ (x, a) \in (0, 1500] \times [ - 1500, 1500] $ when scaled functions are considered and it is larger than $ (0, 500] \times [ - 400, 400] $ for standard IEEE double precision arithmetic. The relative accuracy is better than $ 10^{-13} $ in the range $ (0, 200] \times [ - 200, 200] $ and close to $ 10^{-12} $ in $ (0, 1500] \times [ - 1500, 1500] $.

entry:
@Article{Gil:2004:AMB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 831}: {Modified} {Bessel} functions of
                 imaginary order and positive argument",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "159--164",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992204",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  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 =     "Fortran 77 programs for the computation of modified
                 Bessel functions of purely imaginary order are
                 presented. The codes compute the functions $ K_{ia}(x)
                 $, $ L_{ia}(x) $ and their derivatives for real $a$ and
                 positive $x$; these functions are independent solutions
                 of the differential equation $ x^2 w'' + x w' + (a^2 -
                 x^2)w = 0 $. The code also computes exponentially
                 scaled functions. The range of computation is $ (x, a)
                 \in (0, 1500] \times [ - 1500, 1500] $ when scaled
                 functions are considered and it is larger than $ (0,
                 500] \times [ - 400, 400] $ for standard IEEE double
                 precision arithmetic. The relative accuracy is better
                 than $ 10^{-13} $ in the range $ (0, 200] \times [ -
                 200, 200] $ and close to $ 10^{-12} $ in $ (0, 1500]
                 \times [ - 1500, 1500] $.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Gil:2004:CRZ
author: Amparo Gil and Wolfram Koepf and Javier Segura
title: Computing the Real Zeros of Hypergeometric Functions
journal: j-NUMER-ALGORITHMS
volume: 36
number: 2
pages: 113--134
month: jun
monthnumber: 6
year: 2004
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Dec 6 07:00:32 MST 2004
bibtimestamp: 2004.12.06 07:00:32 MST
URL: http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/54/A/2/abstract.htm
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Amparo Gil and Wolfram Koepf and Javier Segura
rawtitle: Computing the Real Zeros of Hypergeometric Functions
bibsource:
http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

entry:
@Article{Gil:2004:CRZ,
  author =       "Amparo Gil and Wolfram Koepf and Javier Segura",
  title =        "Computing the Real Zeros of Hypergeometric Functions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "36",
  number =       "2",
  pages =        "113--134",
  month =        jun,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 6 07:00:32 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/54/A/2/abstract.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Gil:2004:CSM
author: Amparo Gil and Javier Segura and Nico M. Temme
journal: j-TOMS
volume: 30
number: 2
pages: 145--158
month: jun
monthnumber: 6
year: 2004
CODEN: ACMSCU
DOI: https://doi.org/10.1145/992200.992203
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Jun 10 07:24:58 MDT 2004
bibtimestamp: 2004.06.10 07:24:58 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
title:
Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments

abstract:
We describe a variety of methods to compute the functions $ K_ia(x) $, $ L_ia(x) $ and their derivatives for real $a$ and positive $x$. These functions are numerically satisfactory independent solutions of the differential equation $ x^2 w'' + x w' + (a^2 - x^2)w = 0 $. In the accompanying paper [Gil et al. 2004], we describe the implementation of these methods in Fortran 77 codes.

rawabstract:
We describe a variety of methods to compute the functions $ K_{ia}(x) $, $ L_{ia}(x) $ and their derivatives for real $a$ and positive $x$. These functions are numerically satisfactory independent solutions of the differential equation $ x^2 w'' + x w' + (a^2 - x^2)w = 0 $. In the accompanying paper [Gil et al. 2004], we describe the implementation of these methods in Fortran 77 codes.

rawtitle:
Computing solutions of the modified {Bessel} differential equation for imaginary orders and positive arguments

entry:
@Article{Gil:2004:CSM,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computing solutions of the modified {Bessel}
                 differential equation for imaginary orders and positive
                 arguments",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "145--158",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992203",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  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 =     "We describe a variety of methods to compute the
                 functions $ K_{ia}(x) $, $ L_{ia}(x) $ and their
                 derivatives for real $a$ and positive $x$. These
                 functions are numerically satisfactory independent
                 solutions of the differential equation $ x^2 w'' + x w'
                 + (a^2 - x^2)w = 0 $. In the accompanying paper [Gil et
                 al. 2004], we describe the implementation of these
                 methods in Fortran 77 codes.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Guseinov:2004:EIG
author: I. I. Guseinov and B. A. Mamedov
title: Evaluation of Incomplete Gamma Functions Using Downward Recursion and Analytical Relations
journal: j-J-MATH-CHEM
volume: 36
number: 4
pages: 341--346
month: aug
monthnumber: 8
year: 2004
CODEN: JMCHEG
DOI: https://doi.org/10.1023/B:JOMC.0000044521.18885.d3
ISSN: 0259-9791 (print), 1572-8897 (electronic) OR 02599791 (print), 15728897 (electronic)
ISSNL: 0259-9791 OR 02599791
bibdate: Thu Apr 9 18:14:03 MDT 2015
bibtimestamp: 2015.04.09 18:14:03 MDT
URL: http://link.springer.com/article/10.1023/B:JOMC.0000044521.18885.d3
fjournal: Journal of Mathematical Chemistry
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10910
journalabr: J. Math. Chem.
rawauthor: I. I. Guseinov and B. A. Mamedov
rawtitle: Evaluation of Incomplete Gamma Functions Using Downward Recursion and Analytical Relations
bibsource:
http://link.springer.com/journal/10910/36/4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathchem.bib

entry:
@Article{Guseinov:2004:EIG,
  author =       "I. I. Guseinov and B. A. Mamedov",
  title =        "Evaluation of Incomplete Gamma Functions Using
                 Downward Recursion and Analytical Relations",
  journal =      j-J-MATH-CHEM,
  volume =       "36",
  number =       "4",
  pages =        "341--346",
  month =        aug,
  year =         "2004",
  CODEN =        "JMCHEG",
  DOI =          "https://doi.org/10.1023/B:JOMC.0000044521.18885.d3",
  ISSN =         "0259-9791 (print), 1572-8897 (electronic)",
  ISSN-L =       "0259-9791",
  bibdate =      "Thu Apr 9 18:14:03 MDT 2015",
  bibsource =    "http://link.springer.com/journal/10910/36/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathchem.bib",
  URL =          "http://link.springer.com/article/10.1023/B:JOMC.0000044521.18885.d3",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Chemistry",
  journal-URL =  "http://link.springer.com/journal/10910",
  journalabr =   "J. Math. Chem.",
}


bibtype: misc
filename: elefunt.bib
label: Kahan:2004:LTC
author: W. Kahan
title: A Logarithm Too Clever by Half
pages: 9
day: 9
month: aug
monthnumber: 8
year: 2004
bibdate: Mon Apr 25 17:39:08 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.25 17:39:08 ???
URL: http://www.cs.berkeley.edu/~wkahan/LOG10HAF.TXT
remark: Careful analysis of the problem of computing tt log10(x) accurately from tt log(x).
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: W. Kahan
rawtitle: A Logarithm Too Clever by Half
entry:
@Misc{Kahan:2004:LTC,
  author =       "W. Kahan",
  title =        "A Logarithm Too Clever by Half",
  howpublished = "World-Wide Web document",
  pages =        "9",
  day =          "9",
  month =        aug,
  year =         "2004",
  bibdate =      "Mon Apr 25 17:39:08 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/LOG10HAF.TXT",
  acknowledgement = ack-nhfb,
  remark =       "Careful analysis of the problem of computing {\tt
                 log10(x)} accurately from {\tt log(x)}.",
}


bibtype: article
filename: elefunt.bib
label: Kalmykov:2004:SEH
author: M. Y. Kalmykov
title: Series and $ epsilon $-expansion of the hypergeometric functions
journal: j-NUCL-PHYS-B-PROC-SUPPL
volume: 135
pages: 280--284
year: 2004
CODEN: NPBSE7
ISSN: 0920-5632 (print), 1873-3832 (electronic) OR 09205632 (print), 18733832 (electronic)
ISSNL: 0920-5632 OR 09205632
bibdate: Thu Dec 01 09:14:29 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 09:14:29 ???
fjournal: Nuclear Physics B, Proceedings Supplements
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/09205632
rawauthor: M. Y. Kalmykov
rawtitle: Series and $ \epsilon $-expansion of the hypergeometric functions
entry:
@Article{Kalmykov:2004:SEH,
  author =       "M. Y. Kalmykov",
  title =        "Series and $ \epsilon $-expansion of the
                 hypergeometric functions",
  journal =      j-NUCL-PHYS-B-PROC-SUPPL,
  volume =       "135",
  number =       "??",
  pages =        "280--284",
  month =        "????",
  year =         "2004",
  CODEN =        "NPBSE7",
  ISSN =         "0920-5632 (print), 1873-3832 (electronic)",
  ISSN-L =       "0920-5632",
  bibdate =      "Thu Dec 01 09:14:29 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Nuclear Physics B, Proceedings Supplements",
  journal-URL =  "http://www.sciencedirect.com/science/journal/09205632",
}


bibtype: book
filename: elefunt.bib
label: Kilbas:2004:TTA
author: A. A. (Anatolii Aleksandrovich) Kilbas and Megumi Saigo
title: $H$-transforms: theory and applications
volume: 9
publisher: pub-CHAPMAN-HALL-CRC
address: pub-CHAPMAN-HALL-CRC:adr
pages: xii + 389
year: 2004
ISBN: 0-203-48737-0, 0-415-29916-0, 1-58488-116-X OR 0203487370, 0415299160, 158488116X
bibdate: Sat Oct 30 17:20:21 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.bibsys.no:2100/BIBSYS
bibtimestamp: 2010.10.30 17:20:21 MDT
series: Analytical methods and special functions
subject: $H$-functions; integral transforms
acknowledgement: ack-nhfb
rawauthor: A. A. (Anatolii Aleksandrovich) Kilbas and Megumi Saigo
rawtitle: {$H$}-transforms: theory and applications
ISBN13:
978-0-203-48737-2, 978-1-58488-116-2, 978-0-415-29916-9 OR 9780203487372, 9781584881162, 9780415299169

entry:
@Book{Kilbas:2004:TTA,
  author =       "A. A. (Anatolii Aleksandrovich) Kilbas and Megumi
                 Saigo",
  title =        "{$H$}-transforms: theory and applications",
  volume =       "9",
  publisher =    pub-CHAPMAN-HALL-CRC,
  address =      pub-CHAPMAN-HALL-CRC:adr,
  pages =        "xii + 389",
  year =         "2004",
  ISBN =         "0-203-48737-0, 0-415-29916-0, 1-58488-116-X",
  ISBN-13 =      "978-0-203-48737-2, 978-1-58488-116-2,
                 978-0-415-29916-9",
  LCCN =         "????",
  bibdate =      "Sat Oct 30 17:20:21 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  subject =      "$H$-functions; integral transforms",
}


bibtype: article
filename: elefunt.bib
label: Kyurkchiev:2004:FCN
author: N. Kyurkchiev and A. Iliev
journal: j-COMPUT-MATH-APPL
volume: 47
number: 2--3
pages: 441--446
month: jan
monthnumber: 1
year: 2004
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:49:35 MST 2017
bibtimestamp: 2017.03.01 21:49:35 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122104900363
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: N. Kyurkchiev and A. Iliev
title:
Failure of convergence of the Newton--Weierstrass iterative method for simultaneous root finding of generalized polynomials

rawtitle:
Failure of convergence of the {Newton--Weierstrass} iterative method for simultaneous root finding of generalized polynomials

entry:
@Article{Kyurkchiev:2004:FCN,
  author =       "N. Kyurkchiev and A. Iliev",
  title =        "Failure of convergence of the {Newton--Weierstrass}
                 iterative method for simultaneous root finding of
                 generalized polynomials",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "47",
  number =       "2--3",
  pages =        "441--446",
  month =        jan # "\slash " # feb,
  year =         "2004",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122104900363",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: book
filename: elefunt.bib
label: Lau:2004:NLJ
author: H. T. (Hang Tong) Lau
title: A numerical library in Java for scientists and engineers
publisher: pub-CHAPMAN-HALL-CRC
address: pub-CHAPMAN-HALL-CRC:adr
pages: xxiii + 1063
year: 2004
ISBN: 1-58488-430-4 OR 1584884304
ISBN13: 978-1-58488-430-9 OR 9781584884309
LCCN: QA76.73.J38 L363 2004
bibdate: Fri Sep 26 14:28:47 MDT 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2008.09.26 14:28:47 MDT
URL: http://www.loc.gov/catdir/enhancements/fy0646/2003055149-d.html
subject: Java (Computer program language)
acknowledgement: ack-nhfb
rawauthor: H. T. (Hang Tong) Lau
rawtitle: A numerical library in {Java} for scientists and engineers
entry:
@Book{Lau:2004:NLJ,
  author =       "H. T. (Hang Tong) Lau",
  title =        "A numerical library in {Java} for scientists and
                 engineers",
  publisher =    pub-CHAPMAN-HALL-CRC,
  address =      pub-CHAPMAN-HALL-CRC:adr,
  pages =        "xxiii + 1063",
  year =         "2004",
  ISBN =         "1-58488-430-4",
  ISBN-13 =      "978-1-58488-430-9",
  LCCN =         "QA76.73.J38 L363 2004",
  bibdate =      "Fri Sep 26 14:28:47 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/fy0646/2003055149-d.html",
  acknowledgement = ack-nhfb,
  subject =      "Java (Computer program language)",
}


bibtype: inproceedings
filename: elefunt.bib
label: Markstein:2004:SDS
author: Peter Markstein
title: Software Division and Square Root Using Goldschmidt's Algorithms
crossref: Frougny:2004:RCR
pages: 146--157
year: 2004
bibdate: Fri Nov 17 07:00:31 2023
bibtimestamp: 2023.11.17 07:00:31 ???
URL: http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_12_markstein.pdf
keywords: division; floating-point; Goldschmidt; square root
acknowledgement: ack-nhfb
rawauthor: Peter Markstein
rawtitle: Software Division and Square Root Using {Goldschmidt}'s Algorithms
abstract:
Goldschmidt's Algorithms for division and square root are often characterized as being useful for hardware implementation, and lacking self-correction. A reexamination of these algorithms show that there are good software counterparts that retain the speed advantage of Goldschmidt's Algorithm over the Newton--Raphson iteration. A final step is needed, however, to get the last bit rounded correctly.

rawabstract:
Goldschmidt's Algorithms for division and square root are often characterized as being useful for hardware implementation, and lacking self-correction. A reexamination of these algorithms show that there are good software counterparts that retain the speed advantage of Goldschmidt's Algorithm over the Newton--Raphson iteration. A final step is needed, however, to get the last bit rounded correctly.

entry:
@InProceedings{Markstein:2004:SDS,
  author =       "Peter Markstein",
  title =        "Software Division and Square Root Using
                 {Goldschmidt}'s Algorithms",
  crossref =     "Frougny:2004:RCR",
  pages =        "146--157",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_12_markstein.pdf",
  abstract =     "Goldschmidt's Algorithms for division and square root
                 are often characterized as being useful for hardware
                 implementation, and lacking self-correction. A
                 reexamination of these algorithms show that there are
                 good software counterparts that retain the speed
                 advantage of Goldschmidt's Algorithm over the
                 Newton--Raphson iteration. A final step is needed,
                 however, to get the last bit rounded correctly.",
  acknowledgement = ack-nhfb,
  keywords =     "division; floating-point; Goldschmidt; square root",
}


bibtype: article
filename: elefunt.bib
label: Marsaglia:2004:END
author: George Marsaglia
title: Evaluating the Normal Distribution
journal: j-J-STAT-SOFT
volume: 11
number: 4
pages: 1--7
year: 2004
CODEN: JSSOBK
ISSN: 1548-7660 OR 15487660
bibdate: Sat Dec 04 09:18:40 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.12.04 09:18:40 ???
URL: http://www.jstatsoft.org/counter.php?id=100&url=v11/i04/cphi.pdf&ct=1
fjournal: Journal of Statistical Software
acknowledgement: ack-nhfb
journalURL: http://www.jstatsoft.org/
rawauthor: George Marsaglia
rawtitle: Evaluating the Normal Distribution
remark:
This article exhibits accurate, compact, and fast algorithms for computation of the normal distribution function and the complementary normal distribution, which have a simple relation to the error function and the complementary error function. They appear to be improvements on almost all previously-published algorithms for these functions. However, closer study shows that the complementary normal distribution function has an unchecked out-of-bounds array access for $ |x| geq 17 $, and its Taylor series sum has poor convergence because the tabulated intervals are twice too wide. The Taylor series sum for the normal distribution function is expanded around $ x = 0 $, and thus has poor convergence for large $ |x| $. Neither function takes into account the accuracy loss when the computed result is the larger of the two (their sum is one, and their range is $ [ - infty , + infty ] $ ), although the text discusses the problem. The article also discusses the historical origin of the term ``error function'', tracing it to J. W. Glaisher in 1871.

entry:
@Article{Marsaglia:2004:END,
  author =       "George Marsaglia",
  title =        "Evaluating the Normal Distribution",
  journal =      j-J-STAT-SOFT,
  volume =       "11",
  number =       "4",
  pages =        "1--7",
  month =        "????",
  year =         "2004",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  bibdate =      "Sat Dec 04 09:18:40 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstatsoft.org/counter.php?id=100&url=v11/i04/cphi.pdf&ct=1",
  accepted =     "2004-07-18",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
  remark =       "This article exhibits accurate, compact, and fast
                 algorithms for computation of the normal distribution
                 function and the complementary normal distribution,
                 which have a simple relation to the error function and
                 the complementary error function. They appear to be
                 improvements on almost all previously-published
                 algorithms for these functions. However, closer study
                 shows that the complementary normal distribution
                 function has an unchecked out-of-bounds array access
                 for $ |x| \geq 17 $, and its Taylor series sum has poor
                 convergence because the tabulated intervals are twice
                 too wide. The Taylor series sum for the normal
                 distribution function is expanded around $ x = 0 $, and
                 thus has poor convergence for large $ |x| $. Neither
                 function takes into account the accuracy loss when the
                 computed result is the larger of the two (their sum is
                 one, and their range is $ [ - \infty, + \infty] $ ),
                 although the text discusses the problem. The article
                 also discusses the historical origin of the term
                 ``error function'', tracing it to J. W. Glaisher in
                 1871.",
  submitted =    "2004-06-05",
}


bibtype: article
filename: elefunt.bib
label: Mathar:2004:NRI
author: Richard J. Mathar
title: Numerical Representations of the Incomplete Gamma Function of Complex-Valued Argument
journal: j-NUMER-ALGORITHMS
volume: 36
number: 3
pages: 247--264
month: jul
monthnumber: 7
year: 2004
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Dec 6 07:00:32 MST 2004
bibsource: http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.12.06 07:00:32 MST
URL: http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/57/A/4/abstract.htm
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Richard J. Mathar
rawtitle: Numerical Representations of the Incomplete Gamma Function of Complex-Valued Argument
entry:
@Article{Mathar:2004:NRI,
  author =       "Richard J. Mathar",
  title =        "Numerical Representations of the Incomplete Gamma
                 Function of Complex-Valued Argument",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "36",
  number =       "3",
  pages =        "247--264",
  month =        jul,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 6 07:00:32 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/57/A/4/abstract.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: misc
filename: elefunt.bib
label: Miller:2004:AMF
author: Alan Miller
title: Alan Miller's Fortran Software
pages: 247--264
day: 4
month: feb
monthnumber: 2
year: 2004
bibdate: Tue Jun 13 12:03:37 2023
bibtimestamp: 2023.06.13 12:03:37 ???
note: From the Web site: All code written by Alan Miller is released into the public domain.
URL: https://jblevins.org/mirror/amiller/
acknowledgement: ack-nhfb
howpublished: Web site
rawauthor: Alan Miller
rawnote: From the Web site: All code written by Alan Miller is released into the public domain.
rawtitle: {Alan Miller}'s {Fortran} Software
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib

remark:
The Web site contains a section ``Code converted from the Naval Surface Warfare Center Math. Library'' with links to individual Fortran 90 source files.

entry:
@Misc{Miller:2004:AMF,
  author =       "Alan Miller",
  title =        "{Alan Miller}'s {Fortran} Software",
  howpublished = "Web site",
  day =          "4",
  month =        feb,
  year =         "2004",
  bibdate =      "Tue Jun 13 12:03:37 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib",
  note =         "From the Web site: All code written by Alan Miller is
                 released into the public domain.",
  URL =          "https://jblevins.org/mirror/amiller/",
  acknowledgement = ack-nhfb,
  remark =       "The Web site contains a section ``Code converted from
                 the Naval Surface Warfare Center Math. Library'' with
                 links to individual Fortran 90 source files.",
}


bibtype: article
filename: elefunt.bib
label: Moore:2004:PSW
author: Ian C. Moore and Michael Cada
title: Prolate spheroidal wave functions, an introduction to the Slepian series and its properties
journal: j-APPL-COMPUT-HARMON-ANAL
volume: 16
number: 3
pages: 208--230
month: may
monthnumber: 5
year: 2004
DOI: https://doi.org/10.1016/j.acha.2004.03.004
ISSN: 1063-5203 (print), 1096-603x (electronic) OR 10635203 (print), 1096603x (electronic)
ISSNL: 1063-5203 OR 10635203
bibdate: Sun Oct 31 09:58:00 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.31 09:58:00 ???
keywords: Interpolation; Orthogonal expansion; Prolate spheroidal wave function
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/10635203
rawauthor: Ian C. Moore and Michael Cada
rawtitle: Prolate spheroidal wave functions, an introduction to the {Slepian} series and its properties
abstract:
For decades mathematicians, physicists, and engineers have relied on various orthogonal expansions such as Fourier, Legendre, and Chebyschev to solve a variety of problems. In this paper we exploit the orthogonal properties of prolate spheroidal wave functions (PSWF) in the form of a new orthogonal expansion which we have named the Slepian series. We empirically show that the Slepian series is potentially optimal over more conventional orthogonal expansions for discontinuous functions such as the square wave among others. With regards to interpolation, we explore the connections the Slepian series has to the Shannon sampling theorem. By utilizing Euler's equation, a relationship between the even and odd ordered PSWFs is investigated. We also establish several other key advantages the Slepian series has such as the presence of a free tunable bandwidth parameter.

fjournal:
Applied and Computational Harmonic Analysis. Time-Frequency and Time-Scale Analysis, Wavelets, Numerical Algorithms, and Applications

rawabstract:
For decades mathematicians, physicists, and engineers have relied on various orthogonal expansions such as Fourier, Legendre, and Chebyschev to solve a variety of problems. In this paper we exploit the orthogonal properties of prolate spheroidal wave functions (PSWF) in the form of a new orthogonal expansion which we have named the Slepian series. We empirically show that the Slepian series is potentially optimal over more conventional orthogonal expansions for discontinuous functions such as the square wave among others. With regards to interpolation, we explore the connections the Slepian series has to the Shannon sampling theorem. By utilizing Euler's equation, a relationship between the even and odd ordered PSWFs is investigated. We also establish several other key advantages the Slepian series has such as the presence of a free tunable bandwidth parameter.

entry:
@Article{Moore:2004:PSW,
  author =       "Ian C. Moore and Michael Cada",
  title =        "Prolate spheroidal wave functions, an introduction to
                 the {Slepian} series and its properties",
  journal =      j-APPL-COMPUT-HARMON-ANAL,
  volume =       "16",
  number =       "3",
  pages =        "208--230",
  month =        may,
  year =         "2004",
  DOI =          "https://doi.org/10.1016/j.acha.2004.03.004",
  ISSN =         "1063-5203 (print), 1096-603x (electronic)",
  ISSN-L =       "1063-5203",
  bibdate =      "Sun Oct 31 09:58:00 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "For decades mathematicians, physicists, and engineers
                 have relied on various orthogonal expansions such as
                 Fourier, Legendre, and Chebyschev to solve a variety of
                 problems. In this paper we exploit the orthogonal
                 properties of prolate spheroidal wave functions (PSWF)
                 in the form of a new orthogonal expansion which we have
                 named the Slepian series. We empirically show that the
                 Slepian series is potentially optimal over more
                 conventional orthogonal expansions for discontinuous
                 functions such as the square wave among others. With
                 regards to interpolation, we explore the connections
                 the Slepian series has to the Shannon sampling theorem.
                 By utilizing Euler's equation, a relationship between
                 the even and odd ordered PSWFs is investigated. We also
                 establish several other key advantages the Slepian
                 series has such as the presence of a free tunable
                 bandwidth parameter.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied and Computational Harmonic Analysis.
                 Time-Frequency and Time-Scale Analysis, Wavelets,
                 Numerical Algorithms, and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/10635203",
  keywords =     "Interpolation; Orthogonal expansion; Prolate
                 spheroidal wave function",
}


bibtype: article
filename: elefunt.bib
label: Muller:2004:CSR
author: Siguna Muller
title: On the Computation of Square Roots in Finite Fields
journal: j-DESIGNS-CODES-CRYPTOGR
volume: 31
number: 3
pages: 301--312
month: mar
monthnumber: 3
year: 2004
CODEN: DCCREC
ISSN: 0925-1022 (print), 1573-7586 (electronic) OR 09251022 (print), 15737586 (electronic)
ISSNL: 0925-1022 OR 09251022
bibdate: Tue Aug 3 16:38:18 MDT 2004
bibtimestamp: 2004.08.03 16:38:18 MDT
URL: http://ipsapp008.kluweronline.com/IPS/content/ext/x/J/4630/I/61/A/8/abstract.htm
fjournal: Designs, codes, and cryptography
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10623
rawauthor: Siguna M{\"u}ller
rawtitle: On the Computation of Square Roots in Finite Fields
bibsource:
http://www.wkap.nl/jrnltoc.htm/0925-1022; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Muller:2004:CSR,
  author =       "Siguna M{\"u}ller",
  title =        "On the Computation of Square Roots in Finite Fields",
  journal =      j-DESIGNS-CODES-CRYPTOGR,
  volume =       "31",
  number =       "3",
  pages =        "301--312",
  month =        mar,
  year =         "2004",
  CODEN =        "DCCREC",
  ISSN =         "0925-1022 (print), 1573-7586 (electronic)",
  ISSN-L =       "0925-1022",
  bibdate =      "Tue Aug 3 16:38:18 MDT 2004",
  bibsource =    "http://www.wkap.nl/jrnltoc.htm/0925-1022;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp008.kluweronline.com/IPS/content/ext/x/J/4630/I/61/A/8/abstract.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Designs, codes, and cryptography",
  journal-URL =  "http://link.springer.com/journal/10623",
}


bibtype: article
filename: elefunt.bib
label: Nagel:2004:CEG
author: Bengt Nagel
title: Confluence expansions of the generalized hypergeometric function
journal: j-J-MATH-PHYS
volume: 45
number: 1
pages: 495--508
month: jan
monthnumber: 1
year: 2004
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.1629777
ISSNL: 0022-2488 OR 00222488
bibdate: Tue Oct 25 18:16:52 MDT 2011
bibtimestamp: 2011.10.25 18:16:52 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v45/i1/p495_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
onlinedate: 19 December 2003
rawauthor: Bengt Nagel
rawtitle: Confluence expansions of the generalized hypergeometric function
entry:
@Article{Nagel:2004:CEG,
  author =       "Bengt Nagel",
  title =        "Confluence expansions of the generalized
                 hypergeometric function",
  journal =      j-J-MATH-PHYS,
  volume =       "45",
  number =       "1",
  pages =        "495--508",
  month =        jan,
  year =         "2004",
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  ISSN-L =       "0022-2488",
  bibdate =      "Tue Oct 25 18:16:52 MDT 2011",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v45/i1/p495_s1",
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  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "19 December 2003",
  pagecount =    "14",
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bibtype: inproceedings
filename: elefunt.bib
label: Ortiz:2004:SPI
author: I. Ortiz and M. Jimenez
booktitle: MWSCAS '04. The 2004 47th Midwest Symposium on Circuits and Systems. 25--28 July 2004
title: Scalable pipeline insertion in floating-point division and square root units
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: II-225--II-228
year: 2004
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: I. Ortiz and M. Jimenez
rawbooktitle: {MWSCAS '04. The 2004 47th Midwest Symposium on Circuits and Systems. 25--28 July 2004}
rawtitle: Scalable pipeline insertion in floating-point division and square root units
abstract:
Division and square root are important operations in a number of data processing algorithms. They are inherently time consuming operations and can require a significant amount of resources when implemented in hardware. This work reports the development of scalable, floating-point (FP) division and square root operators with adjustable precision, range, and pipeline granularity. An algorithm for pipeline insertion was used for both operators, enabling speeds up to 204MFLOPS when implemented on a Xilinx Virtex II FPGA.

rawabstract:
Division and square root are important operations in a number of data processing algorithms. They are inherently time consuming operations and can require a significant amount of resources when implemented in hardware. This work reports the development of scalable, floating-point (FP) division and square root operators with adjustable precision, range, and pipeline granularity. An algorithm for pipeline insertion was used for both operators, enabling speeds up to 204MFLOPS when implemented on a Xilinx Virtex II FPGA.

entry:
@InProceedings{Ortiz:2004:SPI,
  author =       "I. Ortiz and M. Jimenez",
  booktitle =    "{MWSCAS '04. The 2004 47th Midwest Symposium on
                 Circuits and Systems. 25--28 July 2004}",
  title =        "Scalable pipeline insertion in floating-point division
                 and square root units",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-225--II-228",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Division and square root are important operations in a
                 number of data processing algorithms. They are
                 inherently time consuming operations and can require a
                 significant amount of resources when implemented in
                 hardware. This work reports the development of
                 scalable, floating-point (FP) division and square root
                 operators with adjustable precision, range, and
                 pipeline granularity. An algorithm for pipeline
                 insertion was used for both operators, enabling speeds
                 up to 204MFLOPS when implemented on a Xilinx Virtex II
                 FPGA.",
  acknowledgement = ack-nhfb,
  summary =      "Division and square root are important operations in a
                 number of data processing algorithms. They are
                 inherently time consuming operations and can require a
                 significant amount of resources when implemented in
                 hardware. This work reports the \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Petkovic:2004:GCS
author: M. S. Petkovic and L. Rancic
title: On the guaranteed convergence of the square-root iteration method
journal: j-J-COMPUT-APPL-MATH
volume: 170
number: 1
pages: 169--179
day: 1
month: sep
monthnumber: 9
year: 2004
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:00:00 MST 2017
bibtimestamp: 2017.02.25 13:00:00 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042704000184
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. S. Petkovi{\'c} and L. Ranci{\'c}
rawtitle: On the guaranteed convergence of the square-root iteration method
entry:
@Article{Petkovic:2004:GCS,
  author =       "M. S. Petkovi{\'c} and L. Ranci{\'c}",
  title =        "On the guaranteed convergence of the square-root
                 iteration method",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "170",
  number =       "1",
  pages =        "169--179",
  day =          "1",
  month =        sep,
  year =         "2004",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:00 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/S0377042704000184",
  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: Pineiro:2004:AAL
author: J. A. Pineiro and M. D. Ercegovac and J. D. Bruguera
title: Algorithm and Architecture for Logarithm, Exponential and Powering Computation
journal: j-IEEE-TRANS-COMPUT
volume: 53
number: 9
pages: 1085--1096
year: 2004
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2004.53
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Jun 24 10:05:48 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.06.24 10:05:48 ???
URL: http://www.ac.usc.es/arquivos/articulos/2004/gac2004-j05.ps
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. A. Pi{\~n}eiro and M. D. Ercegovac and J. D. Bruguera
rawtitle: Algorithm and Architecture for Logarithm, Exponential and Powering Computation
entry:
@Article{Pineiro:2004:AAL,
  author =       "J. A. Pi{\~n}eiro and M. D. Ercegovac and J. D.
                 Bruguera",
  title =        "Algorithm and Architecture for Logarithm, Exponential
                 and Powering Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "9",
  pages =        "1085--1096",
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.53",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 24 10:05:48 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ac.usc.es/arquivos/articulos/2004/gac2004-j05.ps",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
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bibtype: phdthesis
filename: elefunt.bib
label: Pugh:2004:ALG
author: Glendon Ralpha Pugh
title: An Analysis of the Lanczos Gamma Approximation
type: Ph.D. thesis
school: Department of Mathematics, University of British Columbia
address: Vancouver, BC, Canada
pages: viii + 154
year: 2004
ISBN: 0-612-99536-4 OR 0612995364
ISBN13: 978-0-612-99536-9 OR 9780612995369
LCCN: AW5 .B7 2005-995364
bibdate: Mon Nov 24 20:55:30 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2008.11.24 20:55:30 ???
acknowledgement: ack-nhfb
rawauthor: Glendon Ralpha Pugh
rawtitle: An Analysis of the {Lanczos} Gamma Approximation
entry:
@PhdThesis{Pugh:2004:ALG,
  author =       "Glendon Ralpha Pugh",
  title =        "An Analysis of the {Lanczos} Gamma Approximation",
  type =         "Ph.D. thesis",
  school =       "Department of Mathematics, University of British
                 Columbia",
  address =      "Vancouver, BC, Canada",
  pages =        "viii + 154",
  month =        "????",
  year =         "2004",
  ISBN =         "0-612-99536-4",
  ISBN-13 =      "978-0-612-99536-9",
  LCCN =         "AW5 .B7 2005-995364",
  bibdate =      "Mon Nov 24 20:55:30 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Raade:2004:MHS
author: Lennart Raa de and Bertil Westergren
title: Mathematics Handbook for Science and Engineering
publisher: pub-SV
address: pub-SV:adr
edition: Fifth
pages: 562
year: 2004
ISBN: 3-540-21141-1 (hardcover) OR 3540211411 (hardcover)
ISBN13: 978-3-540-21141-9 (hardcover) OR 9783540211419 (hardcover)
LCCN: QA41 .R34 2004
bibdate: Sat May 15 09:15:39 MDT 2010
bibtimestamp: 2010.05.15 09:15:39 MDT
subject: mathematics; formulae; tables; handbooks, manuals, etc.
acknowledgement: ack-nhfb
rawauthor: Lennart R{\aa}de and Bertil Westergren
rawtitle: Mathematics Handbook for Science and Engineering
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager

URL:
http://www.loc.gov/catdir/enhancements/fy0818/2006286513-d.html; http://www.loc.gov/catdir/toc/fy0704/2006286513.html

TOC:
1. Fundamentals Discrete Mathematics / 9 1.1 Logic / 9 1.2 Set Theory / 14 1.3 Binary Relations and Functions / 17 1.4 Algebraic Structures / 21 1.5 Graph Theory / 33 1.6 Codes / 37 2: Algebra / 43 2.1 Basic Algebra of Real Numbers / 43 2.2 Number Theory / 49 2.3 Complex Numbers / 61 2.4 Algebraic Equations / 63 3: Geometry and Trigonometry / 66 3.1 Plane Figures / 66 3.2 Solids / 71 3.3 Spherical Trigonometry / 75 3.4 Geometrical Vectors / 77 3.5 Plane Analytic Geometry / 79 3.6 Analytic Geometry in Space / 83 3.7 Fractals / 87 4: Linear Algebra / 90 4.1 Matrices / 90 4.2 Determinants / 93 4.3 Systems of Linear Equations / 95 4.4 Linear Coordinate Transformations / 97 4.5 Eigenvalues. Diagonalization / 98 4.6 Quadratic Forms / 103 4.7 Linear Spaces / 106 4.8 Linear Mappings / 108 4.9 Tensors / 114 4.10 Complex matrices / 114 5: The Elementary Functions / 118 5.1 A Survey of the Elementary Functions / 118 5.2 Polynomials and Rational Functions / 119 5.3 Logarithmic, Exponential, Power and Hyperbolic Functions / 121 5.4 Trigonometric and Inverse Trigonometric Functions / 125 6: Differential Calculus (one variable) / 132 6.1 Some Basic Concepts / 132 6.2 Limits and Continuity / 133 6.3 Derivatives / 136 6.4 Monotonicity. Extremes of Functions / 139 7: Integral Calculus / 141 7.1 Indefinite Integrals / 141 7.2 Definite Integrals / 146 7.3 Applications of Differential and Integral Calculus / 148 7.4 Table of Indefinite Integral / 153 7.5 Tables of Definite Integrals / 178 8: Sequences and Series / 183 8.1 Sequences of Numbers / 183 8.2 Sequences of Functions / 184 8.3 Series of Constant Terms / 185 8.4 Series of Functions / 187 8.5 Taylor Series / 189 8.6 Special Sums and Series / 192 9: Ordinary Differential Equations (ODE) / 200 9.1 Differential Equations of the First Order / 200 9.2 Differential Equations of the Second Order / 202 9.3 Linear Differential Equations / 205 9.4 Autonomous systems / 2313 9.5 General Concepts and Results / 216 9.6 Linear Difference Equations / 218 10: Multidimensional Calculus / 221 10.1 The Space Rn / 221 10.2 Surfaces. Tangent Planes / 222 10.3 Limits and Continuity / 223 10.4 Partial Derivatives / 224 10.5 Extremes of Functions / 227 10.6 Functions $f: R^n to R^m (R^n to R^n)$ / 229 10.7 Double Integrals / 231 10.8 Triple Integrals / 234 10.9 Partial Differential Equations / 239 11: Vector Analysis / 246 11.1 Curves / 246 11.2 Vector Fields / 248 11.3 Line Integrals / 253 11.4 Surface Integrals / 256 12: Orthogonal Series and Special Functions / 259 12.1 Orthogonal Systems / 259 12.2 Orthogonal Polynomials / 263 12.3 Bernoulli and Euler Polynomials / 269 12.4 Bessel Functions / 270 12.5 Functions Defined by Transcendental Integrals / 287 12.6 Step and Impulse Functions / 297 12.7 Functional Analysis / 298 12.8 Lebesgue Integrals / 303 12.9 Generalized functions (Distributions) / 308 13: Transforms / 310 13.1 Trigonometric Fourier Series / 310 13.2 Fourier Transforms / 315 13.3 Discrete Fourier Transforms / 325 13.4 The $z$-transform / 327 13.5 Laplace Transforms / 330 13.6 Dynamical Systems (Filters) / 338 13.7 Hankel and Hilbert transforms / 341 13.8 Wavelets / 344 14: Complex Analysis / 349 14.1 Functions of a Complex Variable / 349 14.2 Complex Integration / 352 14.3 Power Series Expansions / 354 14.4 Zeros and Singularities / 355 14.5 Conformal Mappings / 356 15: Optimization / 365 15.1 Calculus of Variations / 365 15.2 Linear Optimization / 371 15.3 Integer and Combinatorial Optimization / 379 15.4 Nonlinear Optimization / 383 15.5 Dynamic Optimization / 389 16: Numerical Analysis / 391 16.1 Approximations and Errors / 391 16.2 Numerical Solution of Equations / 392 16.3 Perturbation analysis / 397 16.4 Interpolation / 398 16.5 Numerical Integration and Differentiation / 404 16.6 Numerical Solutions of Differential Equations / 412 16.7 Numerical summation / 421 17: Probability Theory / 424 17.1 Basic Probability Theory / 424 17.2 Probability Distributions / 434 17.3 Stochastic Processes / 439 17.4 Algorithms for Calculation of Probability Distributions / 443 17.5 Simulation / 445 17.6 Queueing Systems / 449 17.7 Reliability / 452 17.8 Tables / 459 18: Statistics / 479 18.1 Descriptive Statistics / 479 18.2 Point Estimation / 488 18.3 Confidence Intervals / 491 18.4 Tables for Confidence Intervals / 495 18.5 Tests of Significance / 501 18.6 Linear Models / 507 18.7 Distribution-free Methods / 512 18.8 Statistical Quality Control / 518 18.9 Factorial Experiments / 522 18.10 Analysis of life time (failure time) data / 525 18.11 Statistical glossary / 526 19: Miscellaneous / 530

rawTOC:
1. Fundamentals \\ Discrete Mathematics / 9 \\ 1.1 Logic / 9 \\ 1.2 Set Theory / 14 \\ 1.3 Binary Relations and Functions / 17 \\ 1.4 Algebraic Structures / 21 \\ 1.5 Graph Theory / 33 \\ 1.6 Codes / 37 \\ 2: Algebra / 43 \\ 2.1 Basic Algebra of Real Numbers / 43 \\ 2.2 Number Theory / 49 \\ 2.3 Complex Numbers / 61 \\ 2.4 Algebraic Equations / 63 \\ 3: Geometry and Trigonometry / 66 \\ 3.1 Plane Figures / 66 \\ 3.2 Solids / 71 \\ 3.3 Spherical Trigonometry / 75 \\ 3.4 Geometrical Vectors / 77 \\ 3.5 Plane Analytic Geometry / 79 \\ 3.6 Analytic Geometry in Space / 83 \\ 3.7 Fractals / 87 \\ 4: Linear Algebra / 90 \\ 4.1 Matrices / 90 \\ 4.2 Determinants / 93 \\ 4.3 Systems of Linear Equations / 95 \\ 4.4 Linear Coordinate Transformations / 97 \\ 4.5 Eigenvalues. Diagonalization / 98 \\ 4.6 Quadratic Forms / 103 \\ 4.7 Linear Spaces / 106 \\ 4.8 Linear Mappings / 108 \\ 4.9 Tensors / 114 \\ 4.10 Complex matrices / 114 \\ 5: The Elementary Functions / 118 \\ 5.1 A Survey of the Elementary Functions / 118 \\ 5.2 Polynomials and Rational Functions / 119 \\ 5.3 Logarithmic, Exponential, Power and Hyperbolic Functions / 121 \\ 5.4 Trigonometric and Inverse Trigonometric Functions / 125 \\ 6: Differential Calculus (one variable) / 132 \\ 6.1 Some Basic Concepts / 132 \\ 6.2 Limits and Continuity / 133 \\ 6.3 Derivatives / 136 \\ 6.4 Monotonicity. Extremes of Functions / 139 \\ 7: Integral Calculus / 141 \\ 7.1 Indefinite Integrals / 141 \\ 7.2 Definite Integrals / 146 \\ 7.3 Applications of Differential and Integral Calculus / 148 \\ 7.4 Table of Indefinite Integral / 153 \\ 7.5 Tables of Definite Integrals / 178 \\ 8: Sequences and Series / 183 \\ 8.1 Sequences of Numbers / 183 \\ 8.2 Sequences of Functions / 184 \\ 8.3 Series of Constant Terms / 185 \\ 8.4 Series of Functions / 187 \\ 8.5 Taylor Series / 189 \\ 8.6 Special Sums and Series / 192 \\ 9: Ordinary Differential Equations (ODE) / 200 \\ 9.1 Differential Equations of the First Order / 200 \\ 9.2 Differential Equations of the Second Order / 202 \\ 9.3 Linear Differential Equations / 205 \\ 9.4 Autonomous systems / 2313 \\ 9.5 General Concepts and Results / 216 \\ 9.6 Linear Difference Equations / 218 \\ 10: Multidimensional Calculus / 221 \\ 10.1 The Space Rn / 221 \\ 10.2 Surfaces. Tangent Planes / 222 \\ 10.3 Limits and Continuity / 223 \\ 10.4 Partial Derivatives / 224 \\ 10.5 Extremes of Functions / 227 \\ 10.6 Functions $f: R^n \to R^m (R^n \to R^n)$ / 229 \\ 10.7 Double Integrals / 231 \\ 10.8 Triple Integrals / 234 \\ 10.9 Partial Differential Equations / 239 \\ 11: Vector Analysis / 246 \\ 11.1 Curves / 246 \\ 11.2 Vector Fields / 248 \\ 11.3 Line Integrals / 253 \\ 11.4 Surface Integrals / 256 \\ 12: Orthogonal Series and Special Functions / 259 \\ 12.1 Orthogonal Systems / 259 \\ 12.2 Orthogonal Polynomials / 263 \\ 12.3 Bernoulli and Euler Polynomials / 269 \\ 12.4 Bessel Functions / 270 \\ 12.5 Functions Defined by Transcendental Integrals / 287 \\ 12.6 Step and Impulse Functions / 297 \\ 12.7 Functional Analysis / 298 \\ 12.8 Lebesgue Integrals / 303 \\ 12.9 Generalized functions (Distributions) / 308 \\ 13: Transforms / 310 \\ 13.1 Trigonometric Fourier Series / 310 \\ 13.2 Fourier Transforms / 315 \\ 13.3 Discrete Fourier Transforms / 325 \\ 13.4 The $z$-transform / 327 \\ 13.5 Laplace Transforms / 330 \\ 13.6 Dynamical Systems (Filters) / 338 \\ 13.7 Hankel and Hilbert transforms / 341 \\ 13.8 Wavelets / 344 \\ 14: Complex Analysis / 349 \\ 14.1 Functions of a Complex Variable / 349 \\ 14.2 Complex Integration / 352 \\ 14.3 Power Series Expansions / 354 \\ 14.4 Zeros and Singularities / 355 \\ 14.5 Conformal Mappings / 356 \\ 15: Optimization / 365 \\ 15.1 Calculus of Variations / 365 \\ 15.2 Linear Optimization / 371 \\ 15.3 Integer and Combinatorial Optimization / 379 \\ 15.4 Nonlinear Optimization / 383 \\ 15.5 Dynamic Optimization / 389 \\ 16: Numerical Analysis / 391 \\ 16.1 Approximations and Errors / 391 \\ 16.2 Numerical Solution of Equations / 392 \\ 16.3 Perturbation analysis / 397 \\ 16.4 Interpolation / 398 \\ 16.5 Numerical Integration and Differentiation / 404 \\ 16.6 Numerical Solutions of Differential Equations / 412 \\ 16.7 Numerical summation / 421 \\ 17: Probability Theory / 424 \\ 17.1 Basic Probability Theory / 424 \\ 17.2 Probability Distributions / 434 \\ 17.3 Stochastic Processes / 439 \\ 17.4 Algorithms for Calculation of Probability Distributions / 443 \\ 17.5 Simulation / 445 \\ 17.6 Queueing Systems / 449 \\ 17.7 Reliability / 452 \\ 17.8 Tables / 459 \\ 18: Statistics / 479 \\ 18.1 Descriptive Statistics / 479 \\ 18.2 Point Estimation / 488 \\ 18.3 Confidence Intervals / 491 \\ 18.4 Tables for Confidence Intervals / 495 \\ 18.5 Tests of Significance / 501 \\ 18.6 Linear Models / 507 \\ 18.7 Distribution-free Methods / 512 \\ 18.8 Statistical Quality Control / 518 \\ 18.9 Factorial Experiments / 522 \\ 18.10 Analysis of life time (failure time) data / 525 \\ 18.11 Statistical glossary / 526 \\ 19: Miscellaneous / 530

entry:
@Book{Raade:2004:MHS,
  author =       "Lennart R{\aa}de and Bertil Westergren",
  title =        "Mathematics Handbook for Science and Engineering",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Fifth",
  pages =        "562",
  year =         "2004",
  ISBN =         "3-540-21141-1 (hardcover)",
  ISBN-13 =      "978-3-540-21141-9 (hardcover)",
  LCCN =         "QA41 .R34 2004",
  bibdate =      "Sat May 15 09:15:39 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0818/2006286513-d.html;
                 http://www.loc.gov/catdir/toc/fy0704/2006286513.html",
  acknowledgement = ack-nhfb,
  libnote =      "Not in my library.",
  subject =      "mathematics; formulae; tables; handbooks, manuals,
                 etc.",
  tableofcontents = "1. Fundamentals \\
                 Discrete Mathematics / 9 \\
                 1.1 Logic / 9 \\
                 1.2 Set Theory / 14 \\
                 1.3 Binary Relations and Functions / 17 \\
                 1.4 Algebraic Structures / 21 \\
                 1.5 Graph Theory / 33 \\
                 1.6 Codes / 37 \\
                 2: Algebra / 43 \\
                 2.1 Basic Algebra of Real Numbers / 43 \\
                 2.2 Number Theory / 49 \\
                 2.3 Complex Numbers / 61 \\
                 2.4 Algebraic Equations / 63 \\
                 3: Geometry and Trigonometry / 66 \\
                 3.1 Plane Figures / 66 \\
                 3.2 Solids / 71 \\
                 3.3 Spherical Trigonometry / 75 \\
                 3.4 Geometrical Vectors / 77 \\
                 3.5 Plane Analytic Geometry / 79 \\
                 3.6 Analytic Geometry in Space / 83 \\
                 3.7 Fractals / 87 \\
                 4: Linear Algebra / 90 \\
                 4.1 Matrices / 90 \\
                 4.2 Determinants / 93 \\
                 4.3 Systems of Linear Equations / 95 \\
                 4.4 Linear Coordinate Transformations / 97 \\
                 4.5 Eigenvalues. Diagonalization / 98 \\
                 4.6 Quadratic Forms / 103 \\
                 4.7 Linear Spaces / 106 \\
                 4.8 Linear Mappings / 108 \\
                 4.9 Tensors / 114 \\
                 4.10 Complex matrices / 114 \\
                 5: The Elementary Functions / 118 \\
                 5.1 A Survey of the Elementary Functions / 118 \\
                 5.2 Polynomials and Rational Functions / 119 \\
                 5.3 Logarithmic, Exponential, Power and Hyperbolic
                 Functions / 121 \\
                 5.4 Trigonometric and Inverse Trigonometric Functions /
                 125 \\
                 6: Differential Calculus (one variable) / 132 \\
                 6.1 Some Basic Concepts / 132 \\
                 6.2 Limits and Continuity / 133 \\
                 6.3 Derivatives / 136 \\
                 6.4 Monotonicity. Extremes of Functions / 139 \\
                 7: Integral Calculus / 141 \\
                 7.1 Indefinite Integrals / 141 \\
                 7.2 Definite Integrals / 146 \\
                 7.3 Applications of Differential and Integral Calculus
                 / 148 \\
                 7.4 Table of Indefinite Integral / 153 \\
                 7.5 Tables of Definite Integrals / 178 \\
                 8: Sequences and Series / 183 \\
                 8.1 Sequences of Numbers / 183 \\
                 8.2 Sequences of Functions / 184 \\
                 8.3 Series of Constant Terms / 185 \\
                 8.4 Series of Functions / 187 \\
                 8.5 Taylor Series / 189 \\
                 8.6 Special Sums and Series / 192 \\
                 9: Ordinary Differential Equations (ODE) / 200 \\
                 9.1 Differential Equations of the First Order / 200 \\
                 9.2 Differential Equations of the Second Order / 202
                 \\
                 9.3 Linear Differential Equations / 205 \\
                 9.4 Autonomous systems / 2313 \\
                 9.5 General Concepts and Results / 216 \\
                 9.6 Linear Difference Equations / 218 \\
                 10: Multidimensional Calculus / 221 \\
                 10.1 The Space Rn / 221 \\
                 10.2 Surfaces. Tangent Planes / 222 \\
                 10.3 Limits and Continuity / 223 \\
                 10.4 Partial Derivatives / 224 \\
                 10.5 Extremes of Functions / 227 \\
                 10.6 Functions $f: R^n \to R^m (R^n \to R^n)$ / 229 \\
                 10.7 Double Integrals / 231 \\
                 10.8 Triple Integrals / 234 \\
                 10.9 Partial Differential Equations / 239 \\
                 11: Vector Analysis / 246 \\
                 11.1 Curves / 246 \\
                 11.2 Vector Fields / 248 \\
                 11.3 Line Integrals / 253 \\
                 11.4 Surface Integrals / 256 \\
                 12: Orthogonal Series and Special Functions / 259 \\
                 12.1 Orthogonal Systems / 259 \\
                 12.2 Orthogonal Polynomials / 263 \\
                 12.3 Bernoulli and Euler Polynomials / 269 \\
                 12.4 Bessel Functions / 270 \\
                 12.5 Functions Defined by Transcendental Integrals /
                 287 \\
                 12.6 Step and Impulse Functions / 297 \\
                 12.7 Functional Analysis / 298 \\
                 12.8 Lebesgue Integrals / 303 \\
                 12.9 Generalized functions (Distributions) / 308 \\
                 13: Transforms / 310 \\
                 13.1 Trigonometric Fourier Series / 310 \\
                 13.2 Fourier Transforms / 315 \\
                 13.3 Discrete Fourier Transforms / 325 \\
                 13.4 The $z$-transform / 327 \\
                 13.5 Laplace Transforms / 330 \\
                 13.6 Dynamical Systems (Filters) / 338 \\
                 13.7 Hankel and Hilbert transforms / 341 \\
                 13.8 Wavelets / 344 \\
                 14: Complex Analysis / 349 \\
                 14.1 Functions of a Complex Variable / 349 \\
                 14.2 Complex Integration / 352 \\
                 14.3 Power Series Expansions / 354 \\
                 14.4 Zeros and Singularities / 355 \\
                 14.5 Conformal Mappings / 356 \\
                 15: Optimization / 365 \\
                 15.1 Calculus of Variations / 365 \\
                 15.2 Linear Optimization / 371 \\
                 15.3 Integer and Combinatorial Optimization / 379 \\
                 15.4 Nonlinear Optimization / 383 \\
                 15.5 Dynamic Optimization / 389 \\
                 16: Numerical Analysis / 391 \\
                 16.1 Approximations and Errors / 391 \\
                 16.2 Numerical Solution of Equations / 392 \\
                 16.3 Perturbation analysis / 397 \\
                 16.4 Interpolation / 398 \\
                 16.5 Numerical Integration and Differentiation / 404
                 \\
                 16.6 Numerical Solutions of Differential Equations /
                 412 \\
                 16.7 Numerical summation / 421 \\
                 17: Probability Theory / 424 \\
                 17.1 Basic Probability Theory / 424 \\
                 17.2 Probability Distributions / 434 \\
                 17.3 Stochastic Processes / 439 \\
                 17.4 Algorithms for Calculation of Probability
                 Distributions / 443 \\
                 17.5 Simulation / 445 \\
                 17.6 Queueing Systems / 449 \\
                 17.7 Reliability / 452 \\
                 17.8 Tables / 459 \\
                 18: Statistics / 479 \\
                 18.1 Descriptive Statistics / 479 \\
                 18.2 Point Estimation / 488 \\
                 18.3 Confidence Intervals / 491 \\
                 18.4 Tables for Confidence Intervals / 495 \\
                 18.5 Tests of Significance / 501 \\
                 18.6 Linear Models / 507 \\
                 18.7 Distribution-free Methods / 512 \\
                 18.8 Statistical Quality Control / 518 \\
                 18.9 Factorial Experiments / 522 \\
                 18.10 Analysis of life time (failure time) data / 525
                 \\
                 18.11 Statistical glossary / 526 \\
                 19: Miscellaneous / 530",
}


bibtype: article
filename: elefunt.bib
label: Skorokhodov:2004:STP
author: S. L. Skorokhodov
journal: j-PROG-COMP-SOFT
volume: 30
number: 3
pages: 150--156
year: 2004
CODEN: PCSODA
ISSN: 0361-7688 (print), 1608-3261 (electronic) OR 03617688 (print), 16083261 (electronic)
ISSNL: 0361-7688 OR 03617688
MRclass: 3C20 (33B15 33C05 33F05 33F10)
MRnumber: MR2082811 (2005f:33013)
bibdate: Thu Dec 01 09:18:16 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 09:18:16 ???
fjournal: Programming and Computer Software; translation of Programmirovaniye (Moscow, USSR) Plenum
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11086
rawauthor: S. L. Skorokhodov
title:
Symbolic transformations in the problem of analytic continuation of the hypergeometric function $_p F_p - 1(z)$ in the neighborhood of the point $ z = 1 $ in the logarithmic case

rawtitle:
Symbolic transformations in the problem of analytic continuation of the hypergeometric function {$_p F_{p - 1}(z)$} in the neighborhood of the point $ z = 1 $ in the logarithmic case

entry:
@Article{Skorokhodov:2004:STP,
  author =       "S. L. Skorokhodov",
  title =        "Symbolic transformations in the problem of analytic
                 continuation of the hypergeometric function {$_p F_{p -
                 1}(z)$} in the neighborhood of the point $ z = 1 $ in
                 the logarithmic case",
  journal =      j-PROG-COMP-SOFT,
  volume =       "30",
  number =       "3",
  pages =        "150--156",
  month =        "????",
  year =         "2004",
  CODEN =        "PCSODA",
  ISSN =         "0361-7688 (print), 1608-3261 (electronic)",
  ISSN-L =       "0361-7688",
  MRclass =      "3C20 (33B15 33C05 33F05 33F10)",
  MRnumber =     "MR2082811 (2005f:33013)",
  bibdate =      "Thu Dec 01 09:18:16 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Programming and Computer Software; translation of
                 Programmirovaniye (Moscow, USSR) Plenum",
  journal-URL =  "http://link.springer.com/journal/11086",
}


bibtype: article
filename: elefunt.bib
label: Thompson:2004:EBB
author: I. J. Thompson
journal: j-COMP-PHYS-COMM
volume: 159
number: 3
pages: 243--244
day: 1
month: jun
monthnumber: 6
year: 2004
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2004.02.007
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Thu Apr 24 10:35:27 2008
bibtimestamp: 2008.04.24 10:35:27 ???
note: See cite Thompson:1987:MBF.
URL: http://www.sciencedirect.com/science/article/pii/S0010465504001067
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: I. J. Thompson
rawnote: See \cite{Thompson:1987:MBF}.
title:
Erratum to booktitle Modified Bessel functions $ I _ n u(z) $ and $ K_nu (z) $ of real order and complex argument [Comput. Phys. Commun. bf 47 (1987) 245--257]

bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib; https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Erratum to {{\booktitle{Modified Bessel functions $ I \_ n u(z) $ and $ K_\nu (z) $ of real order and complex argument}} [Comput. Phys. Commun. {\bf 47} (1987) 245--257]}

entry:
@Article{Thompson:2004:EBB,
  author =       "I. J. Thompson",
  title =        "Erratum to {{\booktitle{Modified Bessel functions $ I
                 \_ n u(z) $ and $ K_\nu (z) $ of real order and complex
                 argument}} [Comput. Phys. Commun. {\bf 47} (1987)
                 245--257]}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "159",
  number =       "3",
  pages =        "243--244",
  day =          "1",
  month =        jun,
  year =         "2004",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2004.02.007",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Apr 24 10:35:27 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Thompson:1987:MBF}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465504001067",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: book
filename: elefunt.bib
label: Vallee:2004:AFA
author: Olivier Vallee and Manuel Soares
title: Airy Functions and Applications to Physics
publisher: pub-WORLD-SCI
address: pub-WORLD-SCI:adr
pages: x + 194
year: 2004
ISBN: 1-86094-478-7 (hardcover) OR 1860944787 (hardcover)
ISBN13: 978-1-86094-478-9 (hardcover) OR 9781860944789 (hardcover)
LCCN: QA351 .V35 2004
bibdate: Tue Dec 5 10:16:05 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.12.05 10:16:05 ???
remark: See also second edition cite Vallee:2010:AFA.
acknowledgement: ack-nhfb
rawauthor: Olivier Vall{\'e}e and Manuel Soares
rawtitle: {Airy} Functions and Applications to Physics
abstract:
The use of special functions, and in particular Airy functions, is rather common in physics. The reason may be found in the need, and even in the necessity, to express a physical phenomenon in terms of an effective and comprehensive analytical form for the whole scientific community. However, for the past twenty years, many physical problems have been resolved by computers. This trend is now becoming the norm as the importance of computers continues to grow. As a last resort, the special functions employed in physics will have to be calculated numerically, even if the analytic formulation of physics is of primary importance.par Airy functions have periodically been the subject of many review articles, but no noteworthy compilation on this subject has been published since the 1950s. In this work, we provide an exhaustive compilation of the current knowledge on the analytical properties of Airy functions, developing with care the calculus implying the Airy functions.

TOC:
Preface / v 1. A Historical Introduction: Sir George Biddell Airy / 1 2. Definitions and Properties / 5 2.1 The Homogeneous Airy Functions / 5 2.1.1 The Airy's equation / 5 2.1.2 Elementary properties / 8 2.1.2.1 Wronskians of homogeneous Airy functions / 8 2.1.2.2 Particular values of Airy functions / 8 2.1.2.3 Relations between Airy functions / 9 2.1.3 Integral representations / 9 2.1.4 Ascending and asymptotic series / 11 2.1.4.1 Expansion of $Ai $ near the origin / 11 2.1.4.2 Ascending series of $Ai $ and $Bi $ / 12 2.1.4.3 Asymptotic series of $Ai $ and $Bi $ / 13 2.2 Properties of Airy Functions / 15 2.2.1 Zeros of Airy functions / 15 2.2.2 The spectral zeta function / 18 2.2.3 Inequalities / 20 2.2.4 Connection with Bessel functions / 20 2.2.5 Modulus and phase of Airy functions / 21 2.2.5.1 Definitions / 21 2.2.5.2 Differential equations / 22 2.2.5.3 Asymptotic expansions / 23 2.2.5.4 Functions of positive arguments / 24 2.3 The Inhomogeneous Airy Functions / 25 2.3.1 Definitions / 25 2.3.2 Properties of inhomogeneous Airy functions / 27 2.3.2.1 Values at the origin / 27 2.3.2.2 Other integral representations / 27 2.3.3 Ascending and asymptotic series / 28 2.3.3.1 Ascending series / 28 2.3.3.2 Asymptotic series / 29 2.3.4 Zeros of the Scorer functions / 29 2.4 Squares and Products of Airy Functions / 30 2.4.1 Differential equation and integral representation / 30 2.4.2 A remarkable identity / 32 2.4.3 The product $Ai (x) Ai (-x)$: Airy wavelets / 32 3. Primitives and Integrals of Airy Functions / 37 3.1 Primitives Containing One Airy Function / 37 3.1.1 In terms of Airy functions / 37 3.1.2 Ascending series / 38 3.1.3 Asymptotic series / 38 3.1.4 Primitive of Scorer functions / 39 3.1.5 Repeated primitives / 40 3.2 Product of Airy Functions / 40 3.2.1 The method of Albright / 41 3.2.2 Some primitives / 43 3.3 Other Primitives / 48 3.4 Miscellaneous / 49 3.5 Elementary Integrals / 50 3.5.1 Particular integrals / 50 3.5.2 Integrals containing a single Airy function / 51 3.5.2.1 Integrals involving algebraic functions / 51 3.5.2.2 Integrals involving transcendental functions / 54 3.5.3 Integrals of products of two Airy functions / 56 3.6 Other Integrals / 60 3.6.1 Integrals involving the Volterra $mu $-function / 60 3.6.2 Canonisation of cubic form / 64 3.6.3 Integrals with three Airy functions / 65 3.6.4 Integrals with four Airy functions / 67 3.6.5 Double integrals / 68 4. Transformations of Airy Functions / 71 4.1 Causal Properties of Airy Functions / 71 4.1.1 Causal relations / 71 4.1.2 Green function of the Airy equation / 73 4.2 The Airy Transform / 74 4.2.1 Definitions and elementary properties / 74 4.2.2 Some examples / 77 4.2.3 Airy polynomials / 82 4.2.4 Summary of Airy transform / 84 4.2.5 Airy averaging / 85 4.3 Other Kinds of Transformations / 85 4.3.1 Laplace transform of Airy functions / 85 4.3.2 Mellin transform of Airy function / 86 4.3.3 Fourier transform of Airy functions / 87 4.4 Expansion into Fourier-Airy Series / 88 5. The Uniform Approximation / 91 5.1 Oscillating Integrals / 91 5.1.1 The method of stationary phase / 91 5.1.2 The uniform approximation of oscillating integrals / 93 5.1.3 The Airy uniform approximation / 94 5.2 Differential Equation of the Second Order / 95 5.2.1 The JWKB method / 95 5.2.2 The generalisation of Langer / 97 5.3 Inhomogeneous Differential Equations / 98 6. Generalisation of Airy Functions / 101 6.1 Generalisation of the Airy Integral / 101 6.2 Third Order Differential Equations / 105 6.2.1 The linear third order differential equation / 105 6.2.2 Asymptotic solutions / 106 6.2.3 The comparison equation / 107 6.3 Differential Equation of the Fourth Order / 111 7. Applications to Classical Physics / 115 7.1 Optics and Electromagnetism / 115 7.2 Fluid Mechanics / 119 7.2.1 The Tricomi equation / 119 7.2.2 The Orr--Sommerfeld equation / 121 7.3 Elasticity / 124 7.4 The Heat Equation / 127 7.5 Nonlinear Physics / 129 7.5.1 Korteweg--de Vries equation / 129 7.5.1.1 The linearised Korteweg--de Vries equation / 129 7.5.1.2 Similarity solutions / 131 7.5.2 The second Painleve equation / 132 7.5.2.1 The Painleve equations / 132 7.5.2.2 An integral equation / 134 7.5.2.3 Rational solutions 135 8. Applications to Quantum Physics / 137 8.1 The Schrodinger Equation / 137 8.1.1 Particle in a uniform field / 137 8.1.2 The $|x|$ potential / 140 8.1.3 Uniform approximation of the Schrodinger equation / 144 8.1.3.1 The JWKB approximation / 145 8.1.3.2 The Airy uniform approximation / 146 8.1.3.3 Exact vs approximate wave functions / 148 8.2 Evaluation of the Franck--Condon Factors / 152 8.2.1 The Franck--Condon principle / 153 8.2.2 The JWKB approximation / 154 8.2.3 The uniform approximation / 157 8.3 The Semiclassical Wigner Distribution / 162 8.3.1 The Weyl--Wigner formalism / 163 8.3.2 The one-dimensional Wigner distribution / 164 8.3.3 The two-dimensional Wigner distribution / 166 8.3.4 Configuration of the Wigner distribution / 169 8.4 Airy Transform of the Schrodinger Equation / 173 Appendix A: Numerical Computation of the Airy Functions / 177 A.1 The Homogeneous Functions / 177 A.2 The Inhomogeneous Functions / 180 Bibliography / 183 Index / 193

rawabstract:
The use of special functions, and in particular Airy functions, is rather common in physics. The reason may be found in the need, and even in the necessity, to express a physical phenomenon in terms of an effective and comprehensive analytical form for the whole scientific community. However, for the past twenty years, many physical problems have been resolved by computers. This trend is now becoming the norm as the importance of computers continues to grow. As a last resort, the special functions employed in physics will have to be calculated numerically, even if the analytic formulation of physics is of primary importance.\par Airy functions have periodically been the subject of many review articles, but no noteworthy compilation on this subject has been published since the 1950s. In this work, we provide an exhaustive compilation of the current knowledge on the analytical properties of Airy functions, developing with care the calculus implying the Airy functions.

shortTOC:
1: A historical introduction: Sir George Biddell Airy / 1 2: Definitions and properties / 5 3: Primitives and integrals of Airy functions / 37 4: Transformations of Airy functions / 71 5: The uniform approximation / 91 6: Generalisation of Airy functions / 101 7: Applications to classical physics / 115 8: Applications to quantum physics / 137 Appendix A: Numerical computation of the Airy functions / 177 Bibliography / 183 Index / 193

rawshortTOC:
1: A historical introduction: Sir George Biddell Airy / 1 \\ 2: Definitions and properties / 5 \\ 3: Primitives and integrals of Airy functions / 37 \\ 4: Transformations of Airy functions / 71 \\ 5: The uniform approximation / 91 \\ 6: Generalisation of Airy functions / 101 \\ 7: Applications to classical physics / 115 \\ 8: Applications to quantum physics / 137 \\ Appendix A: Numerical computation of the Airy functions / 177 \\ Bibliography / 183 \\ Index / 193

rawTOC:
Preface / v \\ 1. A Historical Introduction: Sir George Biddell Airy / 1 \\ 2. Definitions and Properties / 5 \\ 2.1 The Homogeneous Airy Functions / 5 \\ 2.1.1 The Airy's equation / 5 \\ 2.1.2 Elementary properties / 8 \\ 2.1.2.1 Wronskians of homogeneous Airy functions / 8 \\ 2.1.2.2 Particular values of Airy functions / 8 \\ 2.1.2.3 Relations between Airy functions / 9 \\ 2.1.3 Integral representations / 9 \\ 2.1.4 Ascending and asymptotic series / 11 \\ 2.1.4.1 Expansion of $\Ai$ near the origin / 11 \\ 2.1.4.2 Ascending series of $\Ai$ and $\Bi$ / 12 \\ 2.1.4.3 Asymptotic series of $\Ai$ and $\Bi$ / 13 \\ 2.2 Properties of Airy Functions / 15 \\ 2.2.1 Zeros of Airy functions / 15 \\ 2.2.2 The spectral zeta function / 18 \\ 2.2.3 Inequalities / 20 \\ 2.2.4 Connection with Bessel functions / 20 \\ 2.2.5 Modulus and phase of Airy functions / 21 \\ 2.2.5.1 Definitions / 21 \\ 2.2.5.2 Differential equations / 22 \\ 2.2.5.3 Asymptotic expansions / 23 \\ 2.2.5.4 Functions of positive arguments / 24 \\ 2.3 The Inhomogeneous Airy Functions / 25 \\ 2.3.1 Definitions / 25 \\ 2.3.2 Properties of inhomogeneous Airy functions / 27 \\ 2.3.2.1 Values at the origin / 27 \\ 2.3.2.2 Other integral representations / 27 \\ 2.3.3 Ascending and asymptotic series / 28 \\ 2.3.3.1 Ascending series / 28 \\ 2.3.3.2 Asymptotic series / 29 \\ 2.3.4 Zeros of the Scorer functions / 29 \\ 2.4 Squares and Products of Airy Functions / 30 \\ 2.4.1 Differential equation and integral representation / 30 \\ 2.4.2 A remarkable identity / 32 \\ 2.4.3 The product $\Ai(x) \Ai(-x)$: Airy wavelets / 32 \\ 3. Primitives and Integrals of Airy Functions / 37 \\ 3.1 Primitives Containing One Airy Function / 37 \\ 3.1.1 In terms of Airy functions / 37 \\ 3.1.2 Ascending series / 38 \\ 3.1.3 Asymptotic series / 38 \\ 3.1.4 Primitive of Scorer functions / 39 \\ 3.1.5 Repeated primitives / 40 \\ 3.2 Product of Airy Functions / 40 \\ 3.2.1 The method of Albright / 41 \\ 3.2.2 Some primitives / 43 \\ 3.3 Other Primitives / 48 \\ 3.4 Miscellaneous / 49 \\ 3.5 Elementary Integrals / 50 \\ 3.5.1 Particular integrals / 50 \\ 3.5.2 Integrals containing a single Airy function / 51 \\ 3.5.2.1 Integrals involving algebraic functions / 51 \\ 3.5.2.2 Integrals involving transcendental functions / 54 \\ 3.5.3 Integrals of products of two Airy functions / 56 \\ 3.6 Other Integrals / 60 \\ 3.6.1 Integrals involving the Volterra $\mu$-function / 60 \\ 3.6.2 Canonisation of cubic form / 64 \\ 3.6.3 Integrals with three Airy functions / 65 \\ 3.6.4 Integrals with four Airy functions / 67 \\ 3.6.5 Double integrals / 68 \\ 4. Transformations of Airy Functions / 71 \\ 4.1 Causal Properties of Airy Functions / 71 \\ 4.1.1 Causal relations / 71 \\ 4.1.2 Green function of the Airy equation / 73 \\ 4.2 The Airy Transform / 74 \\ 4.2.1 Definitions and elementary properties / 74 \\ 4.2.2 Some examples / 77 \\ 4.2.3 Airy polynomials / 82 \\ 4.2.4 Summary of Airy transform / 84 \\ 4.2.5 Airy averaging / 85 \\ 4.3 Other Kinds of Transformations / 85 \\ 4.3.1 Laplace transform of Airy functions / 85 \\ 4.3.2 Mellin transform of Airy function / 86 \\ 4.3.3 Fourier transform of Airy functions / 87 \\ 4.4 Expansion into Fourier-Airy Series / 88 \\ 5. The Uniform Approximation / 91 \\ 5.1 Oscillating Integrals / 91 \\ 5.1.1 The method of stationary phase / 91 \\ 5.1.2 The uniform approximation of oscillating integrals / 93 \\ 5.1.3 The Airy uniform approximation / 94 \\ 5.2 Differential Equation of the Second Order / 95 \\ 5.2.1 The JWKB method / 95 \\ 5.2.2 The generalisation of Langer / 97 \\ 5.3 Inhomogeneous Differential Equations / 98 \\ 6. Generalisation of Airy Functions / 101 \\ 6.1 Generalisation of the Airy Integral / 101 \\ 6.2 Third Order Differential Equations / 105 \\ 6.2.1 The linear third order differential equation / 105 \\ 6.2.2 Asymptotic solutions / 106 \\ 6.2.3 The comparison equation / 107 \\ 6.3 Differential Equation of the Fourth Order / 111 \\ 7. Applications to Classical Physics / 115 \\ 7.1 Optics and Electromagnetism / 115 \\ 7.2 Fluid Mechanics / 119 \\ 7.2.1 The Tricomi equation / 119 \\ 7.2.2 The Orr--Sommerfeld equation / 121 \\ 7.3 Elasticity / 124 \\ 7.4 The Heat Equation / 127 \\ 7.5 Nonlinear Physics / 129 \\ 7.5.1 Korteweg--de Vries equation / 129 \\ 7.5.1.1 The linearised Korteweg--de Vries equation / 129 \\ 7.5.1.2 Similarity solutions / 131 \\ 7.5.2 The second Painlev{\'e} equation / 132 \\ 7.5.2.1 The Painlev{\'e} equations / 132 \\ 7.5.2.2 An integral equation / 134 \\ 7.5.2.3 Rational solutions 135 \\ 8. Applications to Quantum Physics / 137 \\ 8.1 The Schr{\"o}dinger Equation / 137 \\ 8.1.1 Particle in a uniform field / 137 \\ 8.1.2 The $|x|$ potential / 140 \\ 8.1.3 Uniform approximation of the Schr{\"o}dinger equation / 144 \\ 8.1.3.1 The JWKB approximation / 145 \\ 8.1.3.2 The Airy uniform approximation / 146 \\ 8.1.3.3 Exact vs approximate wave functions / 148 \\ 8.2 Evaluation of the Franck--Condon Factors / 152 \\ 8.2.1 The Franck--Condon principle / 153 \\ 8.2.2 The JWKB approximation / 154 \\ 8.2.3 The uniform approximation / 157 \\ 8.3 The Semiclassical Wigner Distribution / 162 \\ 8.3.1 The Weyl--Wigner formalism / 163 \\ 8.3.2 The one-dimensional Wigner distribution / 164 \\ 8.3.3 The two-dimensional Wigner distribution / 166 \\ 8.3.4 Configuration of the Wigner distribution / 169 \\ 8.4 Airy Transform of the Schr{\"o}dinger Equation / 173 \\ Appendix A: Numerical Computation of the Airy Functions / 177 \\ A.1 The Homogeneous Functions / 177 \\ A.2 The Inhomogeneous Functions / 180 \\ Bibliography / 183 \\ Index / 193

entry:
@Book{Vallee:2004:AFA,
  author =       "Olivier Vall{\'e}e and Manuel Soares",
  title =        "{Airy} Functions and Applications to Physics",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "x + 194",
  year =         "2004",
  ISBN =         "1-86094-478-7 (hardcover)",
  ISBN-13 =      "978-1-86094-478-9 (hardcover)",
  LCCN =         "QA351 .V35 2004",
  bibdate =      "Tue Dec 5 10:16:05 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The use of special functions, and in particular Airy
                 functions, is rather common in physics. The reason may
                 be found in the need, and even in the necessity, to
                 express a physical phenomenon in terms of an effective
                 and comprehensive analytical form for the whole
                 scientific community. However, for the past twenty
                 years, many physical problems have been resolved by
                 computers. This trend is now becoming the norm as the
                 importance of computers continues to grow. As a last
                 resort, the special functions employed in physics will
                 have to be calculated numerically, even if the analytic
                 formulation of physics is of primary
                 importance.\par

                 Airy functions have periodically been the subject of
                 many review articles, but no noteworthy compilation on
                 this subject has been published since the 1950s. In
                 this work, we provide an exhaustive compilation of the
                 current knowledge on the analytical properties of Airy
                 functions, developing with care the calculus implying
                 the Airy functions.",
  acknowledgement = ack-nhfb,
  remark =       "See also second edition \cite{Vallee:2010:AFA}.",
  shorttableofcontents = "1: A historical introduction: Sir George
                 Biddell Airy / 1 \\
                 2: Definitions and properties / 5 \\
                 3: Primitives and integrals of Airy functions / 37 \\
                 4: Transformations of Airy functions / 71 \\
                 5: The uniform approximation / 91 \\
                 6: Generalisation of Airy functions / 101 \\
                 7: Applications to classical physics / 115 \\
                 8: Applications to quantum physics / 137 \\
                 Appendix A: Numerical computation of the Airy functions
                 / 177 \\
                 Bibliography / 183 \\
                 Index / 193",
  tableofcontents = "Preface / v \\
                 1. A Historical Introduction: Sir George Biddell Airy /
                 1 \\
                 2. Definitions and Properties / 5 \\
                 2.1 The Homogeneous Airy Functions / 5 \\
                 2.1.1 The Airy's equation / 5 \\
                 2.1.2 Elementary properties / 8 \\
                 2.1.2.1 Wronskians of homogeneous Airy functions / 8
                 \\
                 2.1.2.2 Particular values of Airy functions / 8 \\
                 2.1.2.3 Relations between Airy functions / 9 \\
                 2.1.3 Integral representations / 9 \\
                 2.1.4 Ascending and asymptotic series / 11 \\
                 2.1.4.1 Expansion of $\Ai$ near the origin / 11 \\
                 2.1.4.2 Ascending series of $\Ai$ and $\Bi$ / 12 \\
                 2.1.4.3 Asymptotic series of $\Ai$ and $\Bi$ / 13 \\
                 2.2 Properties of Airy Functions / 15 \\
                 2.2.1 Zeros of Airy functions / 15 \\
                 2.2.2 The spectral zeta function / 18 \\
                 2.2.3 Inequalities / 20 \\
                 2.2.4 Connection with Bessel functions / 20 \\
                 2.2.5 Modulus and phase of Airy functions / 21 \\
                 2.2.5.1 Definitions / 21 \\
                 2.2.5.2 Differential equations / 22 \\
                 2.2.5.3 Asymptotic expansions / 23 \\
                 2.2.5.4 Functions of positive arguments / 24 \\
                 2.3 The Inhomogeneous Airy Functions / 25 \\
                 2.3.1 Definitions / 25 \\
                 2.3.2 Properties of inhomogeneous Airy functions / 27
                 \\
                 2.3.2.1 Values at the origin / 27 \\
                 2.3.2.2 Other integral representations / 27 \\
                 2.3.3 Ascending and asymptotic series / 28 \\
                 2.3.3.1 Ascending series / 28 \\
                 2.3.3.2 Asymptotic series / 29 \\
                 2.3.4 Zeros of the Scorer functions / 29 \\
                 2.4 Squares and Products of Airy Functions / 30 \\
                 2.4.1 Differential equation and integral representation
                 / 30 \\
                 2.4.2 A remarkable identity / 32 \\
                 2.4.3 The product $\Ai(x) \Ai(-x)$: Airy wavelets / 32
                 \\
                 3. Primitives and Integrals of Airy Functions / 37 \\
                 3.1 Primitives Containing One Airy Function / 37 \\
                 3.1.1 In terms of Airy functions / 37 \\
                 3.1.2 Ascending series / 38 \\
                 3.1.3 Asymptotic series / 38 \\
                 3.1.4 Primitive of Scorer functions / 39 \\
                 3.1.5 Repeated primitives / 40 \\
                 3.2 Product of Airy Functions / 40 \\
                 3.2.1 The method of Albright / 41 \\
                 3.2.2 Some primitives / 43 \\
                 3.3 Other Primitives / 48 \\
                 3.4 Miscellaneous / 49 \\
                 3.5 Elementary Integrals / 50 \\
                 3.5.1 Particular integrals / 50 \\
                 3.5.2 Integrals containing a single Airy function / 51
                 \\
                 3.5.2.1 Integrals involving algebraic functions / 51
                 \\
                 3.5.2.2 Integrals involving transcendental functions /
                 54 \\
                 3.5.3 Integrals of products of two Airy functions / 56
                 \\
                 3.6 Other Integrals / 60 \\
                 3.6.1 Integrals involving the Volterra $\mu$-function /
                 60 \\
                 3.6.2 Canonisation of cubic form / 64 \\
                 3.6.3 Integrals with three Airy functions / 65 \\
                 3.6.4 Integrals with four Airy functions / 67 \\
                 3.6.5 Double integrals / 68 \\
                 4. Transformations of Airy Functions / 71 \\
                 4.1 Causal Properties of Airy Functions / 71 \\
                 4.1.1 Causal relations / 71 \\
                 4.1.2 Green function of the Airy equation / 73 \\
                 4.2 The Airy Transform / 74 \\
                 4.2.1 Definitions and elementary properties / 74 \\
                 4.2.2 Some examples / 77 \\
                 4.2.3 Airy polynomials / 82 \\
                 4.2.4 Summary of Airy transform / 84 \\
                 4.2.5 Airy averaging / 85 \\
                 4.3 Other Kinds of Transformations / 85 \\
                 4.3.1 Laplace transform of Airy functions / 85 \\
                 4.3.2 Mellin transform of Airy function / 86 \\
                 4.3.3 Fourier transform of Airy functions / 87 \\
                 4.4 Expansion into Fourier-Airy Series / 88 \\
                 5. The Uniform Approximation / 91 \\
                 5.1 Oscillating Integrals / 91 \\
                 5.1.1 The method of stationary phase / 91 \\
                 5.1.2 The uniform approximation of oscillating
                 integrals / 93 \\
                 5.1.3 The Airy uniform approximation / 94 \\
                 5.2 Differential Equation of the Second Order / 95 \\
                 5.2.1 The JWKB method / 95 \\
                 5.2.2 The generalisation of Langer / 97 \\
                 5.3 Inhomogeneous Differential Equations / 98 \\
                 6. Generalisation of Airy Functions / 101 \\
                 6.1 Generalisation of the Airy Integral / 101 \\
                 6.2 Third Order Differential Equations / 105 \\
                 6.2.1 The linear third order differential equation /
                 105 \\
                 6.2.2 Asymptotic solutions / 106 \\
                 6.2.3 The comparison equation / 107 \\
                 6.3 Differential Equation of the Fourth Order / 111 \\
                 7. Applications to Classical Physics / 115 \\
                 7.1 Optics and Electromagnetism / 115 \\
                 7.2 Fluid Mechanics / 119 \\
                 7.2.1 The Tricomi equation / 119 \\
                 7.2.2 The Orr--Sommerfeld equation / 121 \\
                 7.3 Elasticity / 124 \\
                 7.4 The Heat Equation / 127 \\
                 7.5 Nonlinear Physics / 129 \\
                 7.5.1 Korteweg--de Vries equation / 129 \\
                 7.5.1.1 The linearised Korteweg--de Vries equation /
                 129 \\
                 7.5.1.2 Similarity solutions / 131 \\
                 7.5.2 The second Painlev{\'e} equation / 132 \\
                 7.5.2.1 The Painlev{\'e} equations / 132 \\
                 7.5.2.2 An integral equation / 134 \\
                 7.5.2.3 Rational solutions 135 \\
                 8. Applications to Quantum Physics / 137 \\
                 8.1 The Schr{\"o}dinger Equation / 137 \\
                 8.1.1 Particle in a uniform field / 137 \\
                 8.1.2 The $|x|$ potential / 140 \\
                 8.1.3 Uniform approximation of the Schr{\"o}dinger
                 equation / 144 \\
                 8.1.3.1 The JWKB approximation / 145 \\
                 8.1.3.2 The Airy uniform approximation / 146 \\
                 8.1.3.3 Exact vs approximate wave functions / 148 \\
                 8.2 Evaluation of the Franck--Condon Factors / 152 \\
                 8.2.1 The Franck--Condon principle / 153 \\
                 8.2.2 The JWKB approximation / 154 \\
                 8.2.3 The uniform approximation / 157 \\
                 8.3 The Semiclassical Wigner Distribution / 162 \\
                 8.3.1 The Weyl--Wigner formalism / 163 \\
                 8.3.2 The one-dimensional Wigner distribution / 164 \\
                 8.3.3 The two-dimensional Wigner distribution / 166 \\
                 8.3.4 Configuration of the Wigner distribution / 169
                 \\
                 8.4 Airy Transform of the Schr{\"o}dinger Equation /
                 173 \\
                 Appendix A: Numerical Computation of the Airy Functions
                 / 177 \\
                 A.1 The Homogeneous Functions / 177 \\
                 A.2 The Inhomogeneous Functions / 180 \\
                 Bibliography / 183 \\
                 Index / 193",
}


bibtype: article
filename: elefunt.bib
label: VanDeun:2004:IAO
author: J. Van Deun and A. Bultheel
title: An Interpolation Algorithm for Orthogonal Rational Functions
journal: j-J-COMPUT-APPL-MATH
volume: 164--165
pages: 749--762
month: mar
monthnumber: 3
year: 2004
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(03)00493-X
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Tue Mar 24 21:14:11 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2009.03.24 21:14:11 ???
fjournal: Journal of Computational and Applied Mathematics
keywords: interpolation; orthogonal polynomials; orthogonal rational functions; three-term recurrence
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: J. {Van Deun} and A. Bultheel
rawtitle: An Interpolation Algorithm for Orthogonal Rational Functions
note:
Proceedings of the 10th International Congress on Computational and Applied Mathematics University of Leuven, Belgium, 22--26 July 2002. Edited by M. J. Goovaerts, S. Vandewalle, and L. Wuytack.

abstract:
Let $ A = alpha _1, alpha _2, ldots $ be a sequence of numbers on the extended real line $ mathcal R = mathcal R union infty $ and $ mu $ a positive bounded Borel measure with support in (a subset of) $ mathcal R $. We introduce rational functions n with poles $ alpha _1, ldots , alpha _n $ that are orthogonal with respect to $ mu $ (if all poles are at infinity, we recover the polynomial situation). It is well known that under certain conditions on the location of the poles, the system $ phi _n $ is regular such that the orthogonal functions satisfy a three-term recurrence relation similar to the one for orthogonal polynomials. To compute the recurrence coefficients one can use explicit formulas involving inner products. We present a theoretical alternative to these explicit formulas that uses certain interpolation properties of the Riesz--Herglotz--Nevanlinna transform $ Omega _mu $ of the measure $ mu $. Error bounds are derived and some examples serve as illustration.

rawabstract:
Let $ A = \{ \alpha_1, \alpha_2, \ldots {} \} $ be a sequence of numbers on the extended real line $ \mathcal {R} = \mathcal {R} \union \{ \infty \} $ and $ \mu $ a positive bounded Borel measure with support in (a subset of) $ \mathcal {R} $. We introduce rational functions n with poles $ \{ \alpha_1, \ldots {}, \alpha_n \} $ that are orthogonal with respect to $ \mu $ (if all poles are at infinity, we recover the polynomial situation). It is well known that under certain conditions on the location of the poles, the system $ \{ \phi_n \} $ is regular such that the orthogonal functions satisfy a three-term recurrence relation similar to the one for orthogonal polynomials. To compute the recurrence coefficients one can use explicit formulas involving inner products. We present a theoretical alternative to these explicit formulas that uses certain interpolation properties of the Riesz--Herglotz--Nevanlinna transform $ \Omega_\mu $ of the measure $ \mu $. Error bounds are derived and some examples serve as illustration.

entry:
@Article{VanDeun:2004:IAO,
  author =       "J. {Van Deun} and A. Bultheel",
  title =        "An Interpolation Algorithm for Orthogonal Rational
                 Functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "164--165",
  number =       "??",
  pages =        "749--762",
  month =        mar,
  year =         "2004",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(03)00493-X",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Tue Mar 24 21:14:11 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the 10th International Congress on
                 Computational and Applied Mathematics University of
                 Leuven, Belgium, 22--26 July 2002. Edited by M. J.
                 Goovaerts, S. Vandewalle, and L. Wuytack.",
  abstract =     "Let $ A = \{ \alpha_1, \alpha_2, \ldots {} \} $ be a
                 sequence of numbers on the extended real line $
                 \mathcal {R} = \mathcal {R} \union \{ \infty \} $ and $
                 \mu $ a positive bounded Borel measure with support in
                 (a subset of) $ \mathcal {R} $. We introduce rational
                 functions n with poles $ \{ \alpha_1, \ldots {},
                 \alpha_n \} $ that are orthogonal with respect to $ \mu
                 $ (if all poles are at infinity, we recover the
                 polynomial situation). It is well known that under
                 certain conditions on the location of the poles, the
                 system $ \{ \phi_n \} $ is regular such that the
                 orthogonal functions satisfy a three-term recurrence
                 relation similar to the one for orthogonal polynomials.
                 To compute the recurrence coefficients one can use
                 explicit formulas involving inner products. We present
                 a theoretical alternative to these explicit formulas
                 that uses certain interpolation properties of the
                 Riesz--Herglotz--Nevanlinna transform $ \Omega_\mu $ of
                 the measure $ \mu $. Error bounds are derived and some
                 examples serve as illustration.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "interpolation; orthogonal polynomials; orthogonal
                 rational functions; three-term recurrence",
}


bibtype: article
filename: elefunt.bib
label: Wang:2004:CHP
author: Ren-Hong Wang and Cheng-de Zheng
title: Cubic Hermite--Pade approximation to the exponential function
journal: j-J-COMPUT-APPL-MATH
volume: 163
number: 1
pages: 259--268
day: 1
month: feb
monthnumber: 2
year: 2004
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:59:56 MST 2017
bibtimestamp: 2017.02.25 12:59:56 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042703008124
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Ren-Hong Wang and Cheng-de Zheng
rawtitle: Cubic {Hermite--Pad{\'e}} approximation to the exponential function
entry:
@Article{Wang:2004:CHP,
  author =       "Ren-Hong Wang and Cheng-de Zheng",
  title =        "Cubic {Hermite--Pad{\'e}} approximation to the
                 exponential function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "163",
  number =       "1",
  pages =        "259--268",
  day =          "1",
  month =        feb,
  year =         "2004",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:59:56 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/S0377042703008124",
  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: Zeng:2004:AMM
author: Zhonggang Zeng
title: Algorithm 835: MultRoot---a Matlab package for computing polynomial roots and multiplicities
journal: j-TOMS
volume: 30
number: 2
pages: 218--236
month: jun
monthnumber: 6
year: 2004
CODEN: ACMSCU
DOI: https://doi.org/10.1145/992200.992209
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65H05
MRnumber: MR2075984 (2005c:65041)
bibdate: Tue Mar 30 16:16:28 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.03.30 16:16:28 ???
fjournal: Association for Computing Machinery. Transactions on Mathematical Software
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Zhonggang Zeng
rawtitle: Algorithm 835: {MultRoot}---a {Matlab} package for computing polynomial roots and multiplicities
abstract:
MultRoot is a collection of Matlab modules for accurate computation of polynomial roots, especially roots with non-trivial multiplicities. As a blackbox-type software, MultRoot requires the polynomial coefficients as the only input, and outputs the computed roots, multiplicities, backward error, estimated forward error, and the structure-preserving condition number. The most significant features of MultRoot are the multiplicity identification capability and high accuracy on multiple roots without using multiprecision arithmetic, even if the polynomial coefficients are inexact. A comprehensive test suite of polynomials that are collected from the literature is included for numerical experiments and performance comparison.

rawabstract:
MultRoot is a collection of Matlab modules for accurate computation of polynomial roots, especially roots with non-trivial multiplicities. As a blackbox-type software, MultRoot requires the polynomial coefficients as the only input, and outputs the computed roots, multiplicities, backward error, estimated forward error, and the structure-preserving condition number. The most significant features of MultRoot are the multiplicity identification capability and high accuracy on multiple roots without using multiprecision arithmetic, even if the polynomial coefficients are inexact. A comprehensive test suite of polynomials that are collected from the literature is included for numerical experiments and performance comparison.

entry:
@Article{Zeng:2004:AMM,
  author =       "Zhonggang Zeng",
  title =        "Algorithm 835: {MultRoot}---a {Matlab} package for
                 computing polynomial roots and multiplicities",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "218--236",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992209",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H05",
  MRnumber =     "MR2075984 (2005c:65041)",
  bibdate =      "Tue Mar 30 16:16:28 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "MultRoot is a collection of Matlab modules for
                 accurate computation of polynomial roots, especially
                 roots with non-trivial multiplicities. As a
                 blackbox-type software, MultRoot requires the
                 polynomial coefficients as the only input, and outputs
                 the computed roots, multiplicities, backward error,
                 estimated forward error, and the structure-preserving
                 condition number. The most significant features of
                 MultRoot are the multiplicity identification capability
                 and high accuracy on multiple roots without using
                 multiprecision arithmetic, even if the polynomial
                 coefficients are inexact. A comprehensive test suite of
                 polynomials that are collected from the literature is
                 included for numerical experiments and performance
                 comparison.",
  acknowledgement = ack-nhfb,
  fjournal =     "Association for Computing Machinery. Transactions on
                 Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Zhu:2004:ISR
author: Hufei Zhu and Zhongding Lei and F. P. S. Chin
title: An improved square-root algorithm for BLAST
journal: j-IEEE-SIGNAL-PROCESS-LETT
volume: 11
number: 9
pages: 772--775
month: sep
monthnumber: 9
year: 2004
CODEN: ISPLEM
DOI: https://doi.org/10.1109/LSP.2004.833483
ISSN: 1070-9908 (print), 1558-2361 (electronic) OR 10709908 (print), 15582361 (electronic)
ISSNL: 1070-9908 OR 10709908
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 Signal Processing Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97
rawauthor: Hufei Zhu and Zhongding Lei and F. P. S. Chin
rawtitle: An improved square-root algorithm for {BLAST}
entry:
@Article{Zhu:2004:ISR,
  author =       "Hufei Zhu and Zhongding Lei and F. P. S. Chin",
  title =        "An improved square-root algorithm for {BLAST}",
  journal =      j-IEEE-SIGNAL-PROCESS-LETT,
  volume =       "11",
  number =       "9",
  pages =        "772--775",
  month =        sep,
  year =         "2004",
  CODEN =        "ISPLEM",
  DOI =          "https://doi.org/10.1109/LSP.2004.833483",
  ISSN =         "1070-9908 (print), 1558-2361 (electronic)",
  ISSN-L =       "1070-9908",
  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 Signal Processing Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97",
  summary =      "In this letter, an improved square-root algorithm for
                 Bell Labs Layered Space-Time (BLAST) system is
                 proposed. It speeds up the original square-root
                 algorithm by 36\% in terms of the number of
                 multiplications and additions. Compared with the
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Abad:2005:TNA
author: Julio Abad and Javier Sesma
title: Two new asymptotic expansions of the ratio of two gamma functions
journal: j-J-COMPUT-APPL-MATH
volume: 173
number: 2
pages: 359--363
day: 15
month: jan
monthnumber: 1
year: 2005
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:00:02 MST 2017
bibtimestamp: 2017.02.25 13:00:02 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042704001669
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Julio Abad and Javier Sesma
rawtitle: Two new asymptotic expansions of the ratio of two gamma functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib

entry:
@Article{Abad:2005:TNA,
  author =       "Julio Abad and Javier Sesma",
  title =        "Two new asymptotic expansions of the ratio of two
                 gamma functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "173",
  number =       "2",
  pages =        "359--363",
  day =          "15",
  month =        jan,
  year =         "2005",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:02 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042704001669",
  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: Antelo:2005:LLD
author: Elisardo Antelo and Tomas Lang and Paolo Montuschi and Alberto Nannarelli
title: Low Latency Digit-Recurrence Reciprocal and Square-Root Reciprocal Algorithm and Architecture
crossref: IEEE:2005:PIS
pages: ??--??
year: 2005
bibdate: Wed Jun 22 07:02:55 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.06.22 07:02:55 ???
URL: http://arith17.polito.it/final/paper-116.pdf
acknowledgement: ack-nhfb
rawauthor: Elisardo Antelo and Tom{\'a}s Lang and Paolo Montuschi and Alberto Nannarelli
rawtitle: Low Latency Digit-Recurrence Reciprocal and Square-Root Reciprocal Algorithm and Architecture
abstract:
The reciprocal and square-root reciprocal operations are important in several applications. For the operations, we present algorithms that combine a digit-by-digit module and one iteration of a quadratic-convergence approximation. The latter is implemented by a digit-recurrence, which uses the digits produced by the digit-by-digit part. In this way, both parts execute in an overlapped manner, so that the total number of cycles is about half the number that would be required by the digit-by-digit part alone. Because of the approximation, correct rounding of the result cannot be obtained directly in all cases; we propose a variable-time implementation that produces the correctly rounded result with a small average overhead. Radix-4 implementations are described and have been synthesized. They achieve the same cycle time as the standard digit-by-digit implementation, resulting in a speed-up of about 2 and, because of the approximation part, the area factor is also about 2. We also show a combined implementation for both operations that has essentially the same complexity as that for square-root reciprocal alone.

rawabstract:
The reciprocal and square-root reciprocal operations are important in several applications. For the operations, we present algorithms that combine a digit-by-digit module and one iteration of a quadratic-convergence approximation. The latter is implemented by a digit-recurrence, which uses the digits produced by the digit-by-digit part. In this way, both parts execute in an overlapped manner, so that the total number of cycles is about half the number that would be required by the digit-by-digit part alone. Because of the approximation, correct rounding of the result cannot be obtained directly in all cases; we propose a variable-time implementation that produces the correctly rounded result with a small average overhead. Radix-4 implementations are described and have been synthesized. They achieve the same cycle time as the standard digit-by-digit implementation, resulting in a speed-up of about 2 and, because of the approximation part, the area factor is also about 2. We also show a combined implementation for both operations that has essentially the same complexity as that for square-root reciprocal alone.

entry:
@InProceedings{Antelo:2005:LLD,
  author =       "Elisardo Antelo and Tom{\'a}s Lang and Paolo Montuschi
                 and Alberto Nannarelli",
  title =        "Low Latency Digit-Recurrence Reciprocal and
                 Square-Root Reciprocal Algorithm and Architecture",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arith17.polito.it/final/paper-116.pdf",
  abstract =     "The reciprocal and square-root reciprocal operations
                 are important in several applications. For the
                 operations, we present algorithms that combine a
                 digit-by-digit module and one iteration of a
                 quadratic-convergence approximation. The latter is
                 implemented by a digit-recurrence, which uses the
                 digits produced by the digit-by-digit part. In this
                 way, both parts execute in an overlapped manner, so
                 that the total number of cycles is about half the
                 number that would be required by the digit-by-digit
                 part alone. Because of the approximation, correct
                 rounding of the result cannot be obtained directly in
                 all cases; we propose a variable-time implementation
                 that produces the correctly rounded result with a small
                 average overhead. Radix-4 implementations are described
                 and have been synthesized. They achieve the same cycle
                 time as the standard digit-by-digit implementation,
                 resulting in a speed-up of about 2 and, because of the
                 approximation part, the area factor is also about 2. We
                 also show a combined implementation for both operations
                 that has essentially the same complexity as that for
                 square-root reciprocal alone.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}


bibtype: book
filename: elefunt.bib
label: Arfken:2005:MMP
author: George B. Arfken and Hans-Jurgen Weber
title: Mathematical Methods for Physicists
publisher: pub-ELSEVIER
address: pub-ELSEVIER:adr
edition: Sixth
pages: xii + 1182
year: 2005
ISBN: 0-12-059876-0, 0-12-088584-0 (paperback) OR 0120598760, 0120885840 (paperback)
ISBN13: 978-0-12-059876-2, 978-0-12-088584-8 (paperback) OR 9780120598762, 9780120885848 (paperback)
LCCN: QA37.3 .A74 2005
bibdate: Tue Feb 17 18:23:45 MST 2009
bibtimestamp: 2009.02.17 18:23:45 MST
subject: Mathematics; Mathematical physics
acknowledgement: ack-nhfb
rawauthor: George B. Arfken and Hans-J{\"u}rgen Weber
rawtitle: Mathematical Methods for Physicists
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager

TOC:
1. Vector Analysis 2. Vector Analysis in Curved Coordinates and Tensors 3. Determinants and Matrices 4. Group Theory 5. Infinite Series 6. Functions of a Complex Variable I: Analytic Properties, Mapping 7. Functions of a Complex Variable II 8. The Gamma Function (Factorial Function) 9. Differential Equations 10. Sturm--Liouville Theory-Orthogonal Functions 11. Bessel Functions 12. Legendre Functions 13. More Special Functions 14. Fourier Series 15. Integral Transforms 16. Integral Equations 17. Calculus of Variations 18. Nonlinear Methods and Chaos 19. Probability

rawTOC:
1. Vector Analysis \\ 2. Vector Analysis in Curved Coordinates and Tensors \\ 3. Determinants and Matrices \\ 4. Group Theory \\ 5. Infinite Series \\ 6. Functions of a Complex Variable I: Analytic Properties, Mapping \\ 7. Functions of a Complex Variable II \\ 8. The Gamma Function (Factorial Function) \\ 9. Differential Equations \\ 10. Sturm--Liouville Theory-Orthogonal Functions \\ 11. Bessel Functions \\ 12. Legendre Functions \\ 13. More Special Functions \\ 14. Fourier Series \\ 15. Integral Transforms \\ 16. Integral Equations \\ 17. Calculus of Variations \\ 18. Nonlinear Methods and Chaos \\ 19. Probability

entry:
@Book{Arfken:2005:MMP,
  author =       "George B. Arfken and Hans-J{\"u}rgen Weber",
  title =        "Mathematical Methods for Physicists",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  edition =      "Sixth",
  pages =        "xii + 1182",
  year =         "2005",
  ISBN =         "0-12-059876-0, 0-12-088584-0 (paperback)",
  ISBN-13 =      "978-0-12-059876-2, 978-0-12-088584-8 (paperback)",
  LCCN =         "QA37.3 .A74 2005",
  bibdate =      "Tue Feb 17 18:23:45 MST 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Mathematical physics",
  tableofcontents = "1. Vector Analysis \\
                 2. Vector Analysis in Curved Coordinates and Tensors
                 \\
                 3. Determinants and Matrices \\
                 4. Group Theory \\
                 5. Infinite Series \\
                 6. Functions of a Complex Variable I: Analytic
                 Properties, Mapping \\
                 7. Functions of a Complex Variable II \\
                 8. The Gamma Function (Factorial Function) \\
                 9. Differential Equations \\
                 10. Sturm--Liouville Theory-Orthogonal Functions \\
                 11. Bessel Functions \\
                 12. Legendre Functions \\
                 13. More Special Functions \\
                 14. Fourier Series \\
                 15. Integral Transforms \\
                 16. Integral Equations \\
                 17. Calculus of Variations \\
                 18. Nonlinear Methods and Chaos \\
                 19. Probability",
  xxauthor =     "George B. (George Brown) Arfken and Hans-J{\"u}rgen
                 Weber",
  xxURL =        "http://www.loc.gov/catdir/enhancements/fy0625/2005049844-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0625/2005049844-t.html",
}


bibtype: article
filename: elefunt.bib
label: Bonan-Hamada:2005:SCF
author: Catherine M. Bonan-Hamada and William B. Jones
title: Stieltjes continued fractions for polygamma functions; speed of convergence
journal: j-J-COMPUT-APPL-MATH
volume: 179
number: 1--2
pages: 47--55
day: 1
month: jul
monthnumber: 7
year: 2005
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:00:05 MST 2017
bibtimestamp: 2017.02.25 13:00:05 MST
URL: http://www.sciencedirect.com/science/article/pii/S037704270400442X
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Catherine M. Bonan-Hamada and William B. Jones
rawtitle: {Stieltjes} continued fractions for polygamma functions; speed of convergence
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib

entry:
@Article{Bonan-Hamada:2005:SCF,
  author =       "Catherine M. Bonan-Hamada and William B. Jones",
  title =        "{Stieltjes} continued fractions for polygamma
                 functions; speed of convergence",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "179",
  number =       "1--2",
  pages =        "47--55",
  day =          "1",
  month =        jul,
  year =         "2005",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:05 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270400442X",
  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: Brisebarre:2005:NRR
author: Nicolas Brisebarre and David Defour and Peter Kornerup and Jean-Michel Muller and Nathalie Revol
title: A New Range-Reduction Algorithm
journal: j-IEEE-TRANS-COMPUT
volume: 54
number: 3
pages: 331--339
month: mar
monthnumber: 3
year: 2005
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2005.36
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Apr 27 18:04:38 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.27 18:04:38 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Nicolas Brisebarre and David Defour and Peter Kornerup and Jean-Michel Muller and Nathalie Revol
rawtitle: A New Range-Reduction Algorithm
URL:
http://csdl.computer.org/comp/trans/tc/2005/03/t0331abs.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0331.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0331.pdf; http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf; http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf?isnumber=30205&prod=JNL&arnumber=1388197&arSt=+331&ared=+339&arAuthor=Brisebarre%2C+N.%3B+Defour%2C+D.%3B+Kornerup%2C+P.%3B+Muller%2C+J.-M.%3B+Revol%2C+N.; http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388197&count=13&index=8; http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388197

abstract:
Range-reduction is a key point for getting accurate elementary function routines. We introduce a new algorithm that is fast for input arguments belonging to the most common domains, yet accurate over the full double-precision range.

rawabstract:
Range-reduction is a key point for getting accurate elementary function routines. We introduce a new algorithm that is fast for input arguments belonging to the most common domains, yet accurate over the full double-precision range.

entry:
@Article{Brisebarre:2005:NRR,
  author =       "Nicolas Brisebarre and David Defour and Peter Kornerup
                 and Jean-Michel Muller and Nathalie Revol",
  title =        "A New Range-Reduction Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "331--339",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.36",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Apr 27 18:04:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0331abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0331.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0331.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf?isnumber=30205&prod=JNL&arnumber=1388197&arSt=+331&ared=+339&arAuthor=Brisebarre%2C+N.%3B+Defour%2C+D.%3B+Kornerup%2C+P.%3B+Muller%2C+J.-M.%3B+Revol%2C+N.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388197&count=13&index=8;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388197",
  abstract =     "Range-reduction is a key point for getting accurate
                 elementary function routines. We introduce a new
                 algorithm that is fast for input arguments belonging to
                 the most common domains, yet accurate over the full
                 double-precision range.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Carlson:2005:JEF
author: B. C. Carlson
title: Jacobian elliptic functions as inverses of an integral
journal: j-J-COMPUT-APPL-MATH
volume: 174
number: 2
pages: 355--359
day: 15
month: feb
monthnumber: 2
year: 2005
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:00:02 MST 2017
bibtimestamp: 2017.02.25 13:00:02 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042704002201
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: B. C. Carlson
rawtitle: {Jacobian} elliptic functions as inverses of an integral
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib

entry:
@Article{Carlson:2005:JEF,
  author =       "B. C. Carlson",
  title =        "{Jacobian} elliptic functions as inverses of an
                 integral",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "174",
  number =       "2",
  pages =        "355--359",
  day =          "15",
  month =        feb,
  year =         "2005",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:02 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042704002201",
  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: Cheng:2005:SEEa
author: Howard Cheng and Barry Gergel and Ethan Kim and Eugene Zima
title: Space-efficient evaluation of hypergeometric series
journal: j-SIGSAM
volume: 39
number: 2
pages: 41--52
month: jun
monthnumber: 6
year: 2005
CODEN: SIGSBZ
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Tue Nov 29 06:11:40 MST 2005
bibtimestamp: 2005.11.29 06:11:40 MST
fjournal: SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
issue: 152
rawauthor: Howard Cheng and Barry Gergel and Ethan Kim and Eugene Zima
rawtitle: Space-efficient evaluation of hypergeometric series
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/sigsam.bib

entry:
@Article{Cheng:2005:SEEa,
  author =       "Howard Cheng and Barry Gergel and Ethan Kim and Eugene
                 Zima",
  title =        "Space-efficient evaluation of hypergeometric series",
  journal =      j-SIGSAM,
  volume =       "39",
  number =       "2",
  pages =        "41--52",
  month =        jun,
  year =         "2005",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Tue Nov 29 06:11:40 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin (ACM Special Interest Group on
                 Symbolic and Algebraic Manipulation)",
  issue =        "152",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}


bibtype: article
filename: elefunt.bib
label: Cheng:2005:SEEb
author: Howard Cheng and Barry Gergel and Ethan Kim and Eugene Zima
title: Space-efficient evaluation of hypergeometric series
journal: j-SIGSAM
volume: 39
number: 3
pages: 81--83
year: 2005
CODEN: SIGSBZ
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Sat Feb 4 09:52:36 MST 2006
bibtimestamp: 2006.02.04 09:52:36 MST
note: ISSAC 2005 poster abstract.
fjournal: SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
issue: 153
rawauthor: Howard Cheng and Barry Gergel and Ethan Kim and Eugene Zima
rawnote: ISSAC 2005 poster abstract.
rawtitle: Space-efficient evaluation of hypergeometric series
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/sigsam.bib

entry:
@Article{Cheng:2005:SEEb,
  author =       "Howard Cheng and Barry Gergel and Ethan Kim and Eugene
                 Zima",
  title =        "Space-efficient evaluation of hypergeometric series",
  journal =      j-SIGSAM,
  volume =       "39",
  number =       "3",
  pages =        "81--83",
  year =         "2005",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Sat Feb 4 09:52:36 MST 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  note =         "ISSAC 2005 poster abstract.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin (ACM Special Interest Group on
                 Symbolic and Algebraic Manipulation)",
  issue =        "153",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}


bibtype: inproceedings
filename: elefunt.bib
label: deDinechin:2005:TPU
author: Florent de Dinechin and Alexey Ershov and Nicolas Gast
title: Towards the Post-ultimate tt libm
crossref: IEEE:2005:PIS
pages: ??--??
year: 2005
bibdate: Wed Jun 22 07:02:55 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.06.22 07:02:55 ???
URL: http://arith17.polito.it/final/paper-165.pdf
acknowledgement: ack-nhfb
rawauthor: Florent de Dinechin and Alexey Ershov and Nicolas Gast
rawtitle: Towards the Post-ultimate {\tt libm}
abstract:
This article presents advances on the subject of correctly rounded elementary functions since the publication of the tt libultim mathematical library developed by Ziv at IBM. This library showed that the average performance and memory overhead of correct rounding could be made negligible. However, the worst-case overhead was still a factor 1000 or more. It is shown here that, with current processor technology, this worst-case overhead can be kept within a factor of 2 to 10 of current best libms. This low overhead has very positive consequences on the techniques for implementing and proving correctly rounded functions, which are also studied. These results lift the last technical obstacles to a generalisation of (at least some) correctly rounded double precision elementary functions.

rawabstract:
This article presents advances on the subject of correctly rounded elementary functions since the publication of the {\tt libultim} mathematical library developed by Ziv at IBM. This library showed that the average performance and memory overhead of correct rounding could be made negligible. However, the worst-case overhead was still a factor 1000 or more. It is shown here that, with current processor technology, this worst-case overhead can be kept within a factor of 2 to 10 of current best libms. This low overhead has very positive consequences on the techniques for implementing and proving correctly rounded functions, which are also studied. These results lift the last technical obstacles to a generalisation of (at least some) correctly rounded double precision elementary functions.

entry:
@InProceedings{deDinechin:2005:TPU,
  author =       "Florent de Dinechin and Alexey Ershov and Nicolas
                 Gast",
  title =        "Towards the Post-ultimate {\tt libm}",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arith17.polito.it/final/paper-165.pdf",
  abstract =     "This article presents advances on the subject of
                 correctly rounded elementary functions since the
                 publication of the {\tt libultim} mathematical library
                 developed by Ziv at IBM. This library showed that the
                 average performance and memory overhead of correct
                 rounding could be made negligible. However, the
                 worst-case overhead was still a factor 1000 or more. It
                 is shown here that, with current processor technology,
                 this worst-case overhead can be kept within a factor of
                 2 to 10 of current best libms. This low overhead has
                 very positive consequences on the techniques for
                 implementing and proving correctly rounded functions,
                 which are also studied. These results lift the last
                 technical obstacles to a generalisation of (at least
                 some) correctly rounded double precision elementary
                 functions.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}


bibtype: article
filename: elefunt.bib
label: Freitas:2005:IPF
author: Pedro Freitas
title: Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums
journal: j-MATH-COMPUT
volume: 74
number: 251
pages: 1425--1440
month: jul
monthnumber: 7
year: 2005
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Aug 2 10:37:19 MDT 2005
bibtimestamp: 2005.08.02 10:37:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Pedro Freitas
rawtitle: Integrals of polylogarithmic functions, recurrence relations, and associated {Euler} sums
bibsource:
http://www.ams.org/mcom/2005-74-251; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2000.bib

URL:
http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/home.html; http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.dvi; http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.pdf; http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.ps; http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.tex

entry:
@Article{Freitas:2005:IPF,
  author =       "Pedro Freitas",
  title =        "Integrals of polylogarithmic functions, recurrence
                 relations, and associated {Euler} sums",
  journal =      j-MATH-COMPUT,
  volume =       "74",
  number =       "251",
  pages =        "1425--1440",
  month =        jul,
  year =         "2005",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Aug 2 10:37:19 MDT 2005",
  bibsource =    "http://www.ams.org/mcom/2005-74-251;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2000.bib",
  URL =          "http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/home.html;
                 http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.dvi;
                 http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.pdf;
                 http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.ps;
                 http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.tex",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Hernandez:2005:ACN
author: M. A. Hernandez and N. Romero
title: Accelerated convergence in Newton's method for approximating square roots
journal: j-J-COMPUT-APPL-MATH
volume: 177
number: 1
pages: 225--229
day: 1
month: may
monthnumber: 5
year: 2005
CODEN: JCAMDI
DOI: https://doi.org/10.1016/j.cam.2004.09.025
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:00:04 MST 2017
bibtimestamp: 2017.02.25 13:00:04 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042704004315
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. A. Hern{\'a}ndez and N. Romero
rawtitle: Accelerated convergence in {Newton}'s method for approximating square roots
entry:
@Article{Hernandez:2005:ACN,
  author =       "M. A. Hern{\'a}ndez and N. Romero",
  title =        "Accelerated convergence in {Newton}'s method for
                 approximating square roots",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "177",
  number =       "1",
  pages =        "225--229",
  day =          "1",
  month =        may,
  year =         "2005",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2004.09.025",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:04 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042704004315",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: misc
filename: elefunt.bib
label: IBM:2005:MAS
author: IBM Corporation
title: Mathematical Acceleration Subsystem for Linux
pages: 225--229
year: 2005
bibdate: Mon Dec 05 18:59:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.12.05 18:59:35 ???
URL: http://www-306.ibm.com/software/awdtools/mass/linux/mass-linux.html
keywords: Mathematical Acceleration Subsystem (MASS)
acknowledgement: ack-nhfb
howpublished: World Wide Web document
rawauthor: {IBM Corporation}
rawtitle: {Mathematical Acceleration Subsystem} for {Linux}
abstract:
Mathematical Acceleration Subsystem (MASS) for Linux consists of libraries of mathematical intrinsic functions tuned specifically for optimum performance on POWER architectures.

remark:
Scalar library functions: atan, atan2, cos, cosh, dnint, exp, log, pow [Fortran **], rsqrt, sin, sinh, sqrt, tan, and tanh.par Vector library double-precision function: vacos, vasin, vatan2, vcbrt, vcos, vcosh, vcosisin, vdint, vdiv, vdnint, vexp, vexpm1, vlog, vlog10, vlog1p, vpow, vrcbrt, vrec, vrsqrt, vsin, vsincos, vsinh, vsqrt, vtan, and vtanh.par Vector library single-precision functions: vsacos, vsasin, vsatan2, vscbrt, vscos, vscosh, vscosisin, vsdiv, vsexp, vsexpm1, vslog, vslog10, vslog1p, vspow, vsrcbrt, vsrec, vsrsqrt, vssin, vssincos, vssinh, vssqrt, vstan, and vstanh.

rawabstract:
Mathematical Acceleration Subsystem (MASS) for Linux consists of libraries of mathematical intrinsic functions tuned specifically for optimum performance on POWER architectures.

entry:
@Misc{IBM:2005:MAS,
  author =       "{IBM Corporation}",
  title =        "{Mathematical Acceleration Subsystem} for {Linux}",
  howpublished = "World Wide Web document",
  year =         "2005",
  bibdate =      "Mon Dec 05 18:59:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www-306.ibm.com/software/awdtools/mass/linux/mass-linux.html",
  abstract =     "Mathematical Acceleration Subsystem (MASS) for Linux
                 consists of libraries of mathematical intrinsic
                 functions tuned specifically for optimum performance on
                 POWER architectures.",
  acknowledgement = ack-nhfb,
  keywords =     "Mathematical Acceleration Subsystem (MASS)",
  remark =       "Scalar library functions: atan, atan2, cos, cosh,
                 dnint, exp, log, pow [Fortran **], rsqrt, sin, sinh,
                 sqrt, tan, and tanh.\par

                 Vector library double-precision function: vacos, vasin,
                 vatan2, vcbrt, vcos, vcosh, vcosisin, vdint, vdiv,
                 vdnint, vexp, vexpm1, vlog, vlog10, vlog1p, vpow,
                 vrcbrt, vrec, vrsqrt, vsin, vsincos, vsinh, vsqrt,
                 vtan, and vtanh.\par

                 Vector library single-precision functions: vsacos,
                 vsasin, vsatan2, vscbrt, vscos, vscosh, vscosisin,
                 vsdiv, vsexp, vsexpm1, vslog, vslog10, vslog1p, vspow,
                 vsrcbrt, vsrec, vsrsqrt, vssin, vssincos, vssinh,
                 vssqrt, vstan, and vstanh.",
}


bibtype: article
filename: elefunt.bib
label: Kornerup:2005:DSS
author: Peter Kornerup
title: Digit Selection for SRT Division and Square Root
journal: j-IEEE-TRANS-COMPUT
volume: 54
number: 3
pages: 294--303
month: mar
monthnumber: 3
year: 2005
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2005.47
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 19 09:20:54 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.19 09:20:54 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Peter Kornerup
rawtitle: Digit Selection for {SRT} Division and Square Root
URL:
http://csdl.computer.org/comp/trans/tc/2005/03/t0294abs.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0294.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0294.pdf; http://ieeexplore.ieee.org/iel5/12/30205/01388194.pdf?isnumber=30205&prod=JNL&arnumber=1388194&arSt=+294&ared=+303&arAuthor=Kornerup%2C+P.; http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388194&count=13&index=5; http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388194

entry:
@Article{Kornerup:2005:DSS,
  author =       "Peter Kornerup",
  title =        "Digit Selection for {SRT} Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "294--303",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.47",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 19 09:20:54 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0294abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0294.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0294.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388194.pdf?isnumber=30205&prod=JNL&arnumber=1388194&arSt=+294&ared=+303&arAuthor=Kornerup%2C+P.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388194&count=13&index=5;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388194",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "The quotient digit selection in the SRT division
                 algorithm is based on a few most significant bits of
                 the remainder and divisor, where the remainder is
                 usually represented in a redundant representation. The
                 number of leading bits needed depends on \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Ledoux:2005:CME
author: V. Ledoux and M. Van Daele and G. Vanden Berghe
title: CP methods and the evaluation of negative energy Coulomb Whittaker functions
journal: j-J-COMPUT-APPL-MATH
volume: 183
number: 1
pages: 168--176
day: 1
month: nov
monthnumber: 11
year: 2005
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:00:34 MST 2017
bibtimestamp: 2017.02.25 13:00:34 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042705000233
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: V. Ledoux and M. {Van Daele} and G. {Vanden Berghe}
rawtitle: {CP} methods and the evaluation of negative energy {Coulomb} {Whittaker} functions
entry:
@Article{Ledoux:2005:CME,
  author =       "V. Ledoux and M. {Van Daele} and G. {Vanden Berghe}",
  title =        "{CP} methods and the evaluation of negative energy
                 {Coulomb} {Whittaker} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "183",
  number =       "1",
  pages =        "168--176",
  day =          "1",
  month =        nov,
  year =         "2005",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:34 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042705000233",
  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: Lee:2005:OHF
author: Dong-U. Lee and Altaf Abdul Gaffar and Oskar Mencer and Wayne Luk
title: Optimizing hardware function evaluation
journal: j-IEEE-TRANS-COMPUT
volume: 54
number: 12
pages: 1520--1531
month: dec
monthnumber: 12
year: 2005
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2005.201
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue May 30 12:04:26 2006
bibtimestamp: 2006.05.30 12:04:26 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Dong-U. Lee and Altaf Abdul Gaffar and Oskar Mencer and Wayne Luk
rawtitle: Optimizing hardware function evaluation
abstract:
We present a methodology and an automated system for function evaluation unit generation. Our system selects the best function evaluation hardware for a given function, accuracy requirements, technology mapping, and optimization metrics, such as area, throughput, and latency. Function evaluation $ f(x) $ typically consists of range reduction and the actual evaluation on a small convenient interval such as $ [0, pi / 2) $ for $ sin (x) $. We investigate the impact of hardware function evaluation with range reduction for a given range and precision of $x$ and $ f(x) $ on area and speed. An automated bit-width optimization technique for minimizing the sizes of the operators in the data paths is also proposed. We explore a vast design space for fixed-point $ sin (x) $, $ log (x) $, and $ sqrt x $ accurate to one unit in the last place using MATLAB and ASC, a stream compiler for field-programmable gate arrays (FPGAs). In this study, we implement over 2,000 placed-and-routed FPGA designs, resulting in over 100 million application-specific integrated circuit (ASIC) equivalent gates. We provide optimal function evaluation results for range and precision combinations between 8 and 48 bits.

keywords:
application specific integrated circuits; application-specific integrated circuit equivalent gates; ASC; ASIC; automated bit-width optimization technique; circuit optimisation; computer arithmetic; elementary function approximation; field programmable gate arrays; field-programmable gate arrays; fixed point arithmetic; fixed-point arithmetic; FPGA; hardware function evaluation optimisation; logic design; MATLAB; minimax approximation; range reduction; stream compiler

rawabstract:
We present a methodology and an automated system for function evaluation unit generation. Our system selects the best function evaluation hardware for a given function, accuracy requirements, technology mapping, and optimization metrics, such as area, throughput, and latency. Function evaluation $ f(x) $ typically consists of range reduction and the actual evaluation on a small convenient interval such as $ [0, \pi / 2) $ for $ \sin (x) $. We investigate the impact of hardware function evaluation with range reduction for a given range and precision of $x$ and $ f(x) $ on area and speed. An automated bit-width optimization technique for minimizing the sizes of the operators in the data paths is also proposed. We explore a vast design space for fixed-point $ \sin (x) $, $ \log (x) $, and $ \sqrt {x} $ accurate to one unit in the last place using MATLAB and ASC, a stream compiler for field-programmable gate arrays (FPGAs). In this study, we implement over 2,000 placed-and-routed FPGA designs, resulting in over 100 million application-specific integrated circuit (ASIC) equivalent gates. We provide optimal function evaluation results for range and precision combinations between 8 and 48 bits.

entry:
@Article{Lee:2005:OHF,
  author =       "Dong-U. Lee and Altaf Abdul Gaffar and Oskar Mencer
                 and Wayne Luk",
  title =        "Optimizing hardware function evaluation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "12",
  pages =        "1520--1531",
  month =        dec,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.201",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue May 30 12:04:26 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  abstract =     "We present a methodology and an automated system for
                 function evaluation unit generation. Our system selects
                 the best function evaluation hardware for a given
                 function, accuracy requirements, technology mapping,
                 and optimization metrics, such as area, throughput, and
                 latency. Function evaluation $ f(x) $ typically
                 consists of range reduction and the actual evaluation
                 on a small convenient interval such as $ [0, \pi / 2) $
                 for $ \sin (x) $. We investigate the impact of hardware
                 function evaluation with range reduction for a given
                 range and precision of $x$ and $ f(x) $ on area and
                 speed. An automated bit-width optimization technique
                 for minimizing the sizes of the operators in the data
                 paths is also proposed. We explore a vast design space
                 for fixed-point $ \sin (x) $, $ \log (x) $, and $ \sqrt
                 {x} $ accurate to one unit in the last place using
                 MATLAB and ASC, a stream compiler for
                 field-programmable gate arrays (FPGAs). In this study,
                 we implement over 2,000 placed-and-routed FPGA designs,
                 resulting in over 100 million application-specific
                 integrated circuit (ASIC) equivalent gates. We provide
                 optimal function evaluation results for range and
                 precision combinations between 8 and 48 bits.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "application specific integrated circuits;
                 application-specific integrated circuit equivalent
                 gates; ASC; ASIC; automated bit-width optimization
                 technique; circuit optimisation; computer arithmetic;
                 elementary function approximation; field programmable
                 gate arrays; field-programmable gate arrays; fixed
                 point arithmetic; fixed-point arithmetic; FPGA;
                 hardware function evaluation optimisation; logic
                 design; MATLAB; minimax approximation; range reduction;
                 stream compiler",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lefevre:2005:NRD
author: Vincent Lefevre
title: New Results on the Distance Between a Segment and $ Z^2 $. Application to the Exact Rounding
crossref: IEEE:2005:PIS
pages: ??--??
year: 2005
bibdate: Wed Jun 22 07:02:55 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.06.22 07:02:55 ???
URL: http://arith17.polito.it/final/paper-147.pdf
acknowledgement: ack-nhfb
rawauthor: Vincent Lef{\`e}vre
rawtitle: New Results on the Distance Between a Segment and {$ Z^2 $}. {Application} to the Exact Rounding
abstract:
This paper presents extensions to Lefevre's algorithm that computes a lower bound on the distance between a segment and a regular grid $ Z^2 $. This algorithm and, in particular, the extensions are useful in the search for worst cases for the exact rounding of unary elementary functions or base-conversion functions. The proof that is presented here is simpler and less technical than the original proof. This paper also gives benchmark results with various optimization parameters, explanations of these results, and an application to base conversion.

rawabstract:
This paper presents extensions to Lef{\'e}vre's algorithm that computes a lower bound on the distance between a segment and a regular grid $ Z^2 $. This algorithm and, in particular, the extensions are useful in the search for worst cases for the exact rounding of unary elementary functions or base-conversion functions. The proof that is presented here is simpler and less technical than the original proof. This paper also gives benchmark results with various optimization parameters, explanations of these results, and an application to base conversion.

entry:
@InProceedings{Lefevre:2005:NRD,
  author =       "Vincent Lef{\`e}vre",
  title =        "New Results on the Distance Between a Segment and {$
                 Z^2 $}. {Application} to the Exact Rounding",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arith17.polito.it/final/paper-147.pdf",
  abstract =     "This paper presents extensions to Lef{\'e}vre's
                 algorithm that computes a lower bound on the distance
                 between a segment and a regular grid $ Z^2 $. This
                 algorithm and, in particular, the extensions are useful
                 in the search for worst cases for the exact rounding of
                 unary elementary functions or base-conversion
                 functions. The proof that is presented here is simpler
                 and less technical than the original proof. This paper
                 also gives benchmark results with various optimization
                 parameters, explanations of these results, and an
                 application to base conversion.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}


bibtype: inproceedings
filename: elefunt.bib
label: Markstein:2005:FSM
author: Peter Markstein
title: A Fast-Start Method for Computing the Inverse Tangent
crossref: IEEE:2005:PIS
pages: ??--??
year: 2005
bibdate: Wed Jun 22 07:02:55 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.06.22 07:02:55 ???
URL: http://arith17.polito.it/final/paper-112.pdf
keywords: IA-64; Itanium-2
acknowledgement: ack-nhfb
rawauthor: Peter Markstein
rawtitle: A Fast-Start Method for Computing the Inverse Tangent
abstract:
In a search for an algorithm to compute $ atan (x) $ which has both low latency and few floating point instructions, an interesting variant of familiar trigonometry formulas was discovered that allow the start of argument reduction to commence before any references to tables stored in memory are needed. Low latency makes the method suitable for a closed subroutine, and few floating point operations make the method advantageous for a software-pipelined implementation.

rawabstract:
In a search for an algorithm to compute $ \atan (x) $ which has both low latency and few floating point instructions, an interesting variant of familiar trigonometry formulas was discovered that allow the start of argument reduction to commence before any references to tables stored in memory are needed. Low latency makes the method suitable for a closed subroutine, and few floating point operations make the method advantageous for a software-pipelined implementation.

entry:
@InProceedings{Markstein:2005:FSM,
  author =       "Peter Markstein",
  title =        "A Fast-Start Method for Computing the Inverse
                 Tangent",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arith17.polito.it/final/paper-112.pdf",
  abstract =     "In a search for an algorithm to compute $ \atan (x) $
                 which has both low latency and few floating point
                 instructions, an interesting variant of familiar
                 trigonometry formulas was discovered that allow the
                 start of argument reduction to commence before any
                 references to tables stored in memory are needed. Low
                 latency makes the method suitable for a closed
                 subroutine, and few floating point operations make the
                 method advantageous for a software-pipelined
                 implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "IA-64; Itanium-2",
  pagecount =    "6",
}


bibtype: article
filename: elefunt.bib
label: Merkle:2005:GRG
author: M. Merkle
title: Gurland's ratio for the gamma function
journal: j-COMPUT-MATH-APPL
volume: 49
number: 2--3
pages: 389--406
month: jan
monthnumber: 1
year: 2005
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:49:42 MST 2017
bibtimestamp: 2017.03.01 21:49:42 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122105000416
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: M. Merkle
rawtitle: {Gurland}'s ratio for the gamma function
entry:
@Article{Merkle:2005:GRG,
  author =       "M. Merkle",
  title =        "{Gurland}'s ratio for the gamma function",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "49",
  number =       "2--3",
  pages =        "389--406",
  month =        jan # "\slash " # feb,
  year =         "2005",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:42 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122105000416",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Perram:2005:EFW
author: John W. Perram and Edgar R. Smith
title: Elliptic Functions of the Worst Kind: Non-linear Quantisation of the Classical Spherical Pendulum
journal: j-ADV-QUANTUM-CHEM
volume: 48
pages: 111--125
year: 2005
CODEN: AQCHA9
DOI: https://doi.org/10.1016/S0065-3276(05)48008-9
ISSN: 0065-3276 OR 00653276
ISSNL: 0065-3276 OR 00653276
bibdate: Thu Oct 13 11:45:04 MDT 2011
bibtimestamp: 2011.10.13 11:45:04 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0065327605480089
fjournal: Advances in Quantum Chemistry
acknowledgement: ack-nhfb
ajournal: Adv. Quantum Chem.
journalURL: http://www.sciencedirect.com/science/bookseries/00653276
rawauthor: John W. Perram and Edgar R. Smith
rawtitle: Elliptic Functions of the Worst Kind: Non-linear Quantisation of the Classical Spherical Pendulum
bibsource:
http://www.sciencedirect.com/science/bookseries/00653276; https://www.math.utah.edu/pub/tex/bib/advquantumchem.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Perram:2005:EFW,
  author =       "John W. Perram and Edgar R. Smith",
  title =        "Elliptic Functions of the Worst Kind: Non-linear
                 Quantisation of the Classical Spherical Pendulum",
  journal =      j-ADV-QUANTUM-CHEM,
  volume =       "48",
  pages =        "111--125",
  year =         "2005",
  CODEN =        "AQCHA9",
  DOI =          "https://doi.org/10.1016/S0065-3276(05)48008-9",
  ISSN =         "0065-3276",
  ISSN-L =       "0065-3276",
  bibdate =      "Thu Oct 13 11:45:04 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/bookseries/00653276;
                 https://www.math.utah.edu/pub/tex/bib/advquantumchem.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0065327605480089",
  acknowledgement = ack-nhfb,
  ajournal =     "Adv. Quantum Chem.",
  fjournal =     "Advances in Quantum Chemistry",
  journal-URL =  "http://www.sciencedirect.com/science/bookseries/00653276",
}


bibtype: article
filename: elefunt.bib
label: Pineiro:2005:HSF
author: Jose-Alejandro Pineiro and Stuart F. Oberman and Jean-Michel Muller and Javier D. Bruguera
title: High-Speed Function Approximation Using a Minimax Quadratic Interpolator
journal: j-IEEE-TRANS-COMPUT
volume: 54
number: 3
pages: 304--318
month: mar
monthnumber: 3
year: 2005
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2005.52
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 19 09:20:54 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.19 09:20:54 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Jose-Alejandro Pi{\~n}eiro and Stuart F. Oberman and Jean-Michel Muller and Javier D. Bruguera
rawtitle: High-Speed Function Approximation Using a Minimax Quadratic Interpolator
URL:
http://csdl.computer.org/comp/trans/tc/2005/03/t0304abs.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0304.htm; http://csdl.computer.org/dl/trans/tc/2005/03/t0304.pdf; http://ieeexplore.ieee.org/iel5/12/30205/01388195.pdf?isnumber=30205&prod=JNL&arnumber=1388195&arSt=+304&ared=+318&arAuthor=Pineiro%2C+J.-A.%3B+Oberman%2C+S.F.%3B+Muller%2C+J.-M.%3B+Bruguera%2C+J.D.; http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388195&count=13&index=6; http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388195

abstract:
A table-based method for high-speed function approximation in single-precision floating-point format is presented in this paper. Our focus is the approximation of reciprocal, square root, square root reciprocal, exponentials, logarithms, trigonometric functions, powering (with a fixed exponent $p$ ), or special functions. The algorithm presented here combines table look-up, an enhanced minimax quadratic approximation, and an efficient evaluation of the second-degree polynomial (using a specialized squaring unit, redundant arithmetic, and multioperand addition). The execution times and area costs of an architecture implementing our method are estimated, showing the achievement of the fast execution times of linear approximation methods and the reduced area requirements of other second-degree interpolation algorithms. Moreover, the use of an enhanced minimax approximation which, through an iterative process, takes into account the effect of rounding the polynomial coefficients to a finite size allows for a further reduction in the size of the look-up tables to be used, making our method very suitable for the implementation of an elementary function generator in state-of-the-art DSPs or graphics processing units (GPUs).

rawabstract:
A table-based method for high-speed function approximation in single-precision floating-point format is presented in this paper. Our focus is the approximation of reciprocal, square root, square root reciprocal, exponentials, logarithms, trigonometric functions, powering (with a fixed exponent $p$ ), or special functions. The algorithm presented here combines table look-up, an enhanced minimax quadratic approximation, and an efficient evaluation of the second-degree polynomial (using a specialized squaring unit, redundant arithmetic, and multioperand addition). The execution times and area costs of an architecture implementing our method are estimated, showing the achievement of the fast execution times of linear approximation methods and the reduced area requirements of other second-degree interpolation algorithms. Moreover, the use of an enhanced minimax approximation which, through an iterative process, takes into account the effect of rounding the polynomial coefficients to a finite size allows for a further reduction in the size of the look-up tables to be used, making our method very suitable for the implementation of an elementary function generator in state-of-the-art DSPs or graphics processing units (GPUs).

entry:
@Article{Pineiro:2005:HSF,
  author =       "Jose-Alejandro Pi{\~n}eiro and Stuart F. Oberman and
                 Jean-Michel Muller and Javier D. Bruguera",
  title =        "High-Speed Function Approximation Using a Minimax
                 Quadratic Interpolator",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "304--318",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.52",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 19 09:20:54 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0304abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0304.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0304.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388195.pdf?isnumber=30205&prod=JNL&arnumber=1388195&arSt=+304&ared=+318&arAuthor=Pineiro%2C+J.-A.%3B+Oberman%2C+S.F.%3B+Muller%2C+J.-M.%3B+Bruguera%2C+J.D.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388195&count=13&index=6;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388195",
  abstract =     "A table-based method for high-speed function
                 approximation in single-precision floating-point format
                 is presented in this paper. Our focus is the
                 approximation of reciprocal, square root, square root
                 reciprocal, exponentials, logarithms, trigonometric
                 functions, powering (with a fixed exponent $p$ ), or
                 special functions. The algorithm presented here
                 combines table look-up, an enhanced minimax quadratic
                 approximation, and an efficient evaluation of the
                 second-degree polynomial (using a specialized squaring
                 unit, redundant arithmetic, and multioperand addition).
                 The execution times and area costs of an architecture
                 implementing our method are estimated, showing the
                 achievement of the fast execution times of linear
                 approximation methods and the reduced area requirements
                 of other second-degree interpolation algorithms.
                 Moreover, the use of an enhanced minimax approximation
                 which, through an iterative process, takes into account
                 the effect of rounding the polynomial coefficients to a
                 finite size allows for a further reduction in the size
                 of the look-up tables to be used, making our method
                 very suitable for the implementation of an elementary
                 function generator in state-of-the-art DSPs or graphics
                 processing units (GPUs).",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


