validated computing

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… … ► 1969 in Villarrobledo, Spain) is Associate Professor in the Department of Applied Mathematics and Computer Science in the Universidad de Cantabria, Spain. … ►Gil served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions. …

13: David M. Bressoud

… … ► 227, in 1980, Factorization and Primality Testing, published by Springer-Verlag in 1989, Second Year Calculus from Celestial Mechanics to Special Relativity, published by Springer-Verlag in 1992, A Radical Approach to Real Analysis, published by the Mathematical Association of America in 1994, with a second edition in 2007, Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture, published by the Mathematical Association of America and Cambridge University Press in 1999, A Course in Computational Number Theory (with S. … ►Bressoud served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions.

14: Bille C. Carlson

… ►Symmetric integrals and their degenerate cases allow greatly shortened integral tables and improved algorithms for numerical computation. … ►In Symmetry in c, d, n of Jacobian elliptic functions (2004) he found a previously hidden symmetry in relations between Jacobian elliptic functions, which can now take a form that remains valid when the letters c, d, and n are permuted. … ►Carlson served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions.

15: Mathematical Introduction

… ►This part of the project has been carried out by a team comprising the mathematics editor, authors, validators, and the NIST professional staff. … ►First, the editors instituted a validation process for the whole technical content of each chapter. …All chapters went through several drafts (nine in some cases) before the authors, validators, and editors were fully satisfied. … ►The first three chapters of the NIST Handbook and DLMF are methodology chapters that provide detailed coverage of, and references for, mathematical topics that are especially important in the theory, computation, and application of special functions. … ►

Computation

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16: Ranjan Roy

… … ► Huffer Professor of Mathematics and Astronomy at Beloit College, Beloit, Wisconsin and at the time of his death was the chair of the Mathematics and Computer Science Department. … ►Roy served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions. …

17: Nico M. Temme

… ►He has served on the editorial boards of the SIAM Journal on Mathematical Analysis, Mathematics of Computation, ZAMP, and Integral Transforms and Special Functions. In July 2005, a conference Special Functions: Asymptotic Analysis and Computation was held in Santander, Spain, to celebrate his 65th birthday. … ►He also served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions. …

18: Tom H. Koornwinder

… ►Koornwinder has published numerous papers on special functions, harmonic analysis, Lie groups, quantum groups, computer algebra, and their interrelations, including an interpretation of Askey–Wilson polynomials on quantum SU(2), and a five-parameter extension (the Macdonald–Koornwinder polynomials) of Macdonald’s polynomials for root systems BC. … ►Koornwinder served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions. …

19: 6.20 Approximations

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Luke (1969b, p. 25) gives a Chebyshev expansion near infinity for the confluent hypergeometric $U$ -function (§13.2(i)) from which Chebyshev expansions near infinity for $E_{1}\left(z\right)$ , $\mathrm{f}\left(z\right)$ , and $\mathrm{g}\left(z\right)$ follow by using (6.11.2) and (6.11.3). Luke also includes a recursion scheme for computing the coefficients in the expansions of the $U$ functions. If $|\operatorname{ph}z|<\pi$ the scheme can be used in backward direction.

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Luke (1969b, pp. 402, 410, and 415–421) gives main diagonal Padé approximations for $\operatorname{Ein}\left(z\right)$ , $\operatorname{Si}\left(z\right)$ , $\operatorname{Cin}\left(z\right)$ (valid near the origin), and $E_{1}\left(z\right)$ (valid for large $|z|$ ); approximate errors are given for a selection of $z$ -values.

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20: Tom M. Apostol

… ►He was internationally known for his textbooks on calculus, analysis, and analytic number theory, which have been translated into five languages, and for creating Project MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects. … ►Apostol served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions.