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21: 24.20 Tables

… ►Wagstaff (1978) gives complete prime factorizations of $N_n$ and $E_n$ for $n=20(2)60$ and $n=8(2)42$, respectively. In Wagstaff (2002) these results are extended to $n=60(2)152$ and $n=40(2)88$, respectively, with further complete and partial factorizations listed up to $n=300$ and $n=200$, respectively. …

22: Morris Newman

… … ► 1924 in Brooklyn, New York, d.  2007) received his early training in mathematics from New York University and Columbia University, obtaining his Ph. …from the University of Pennsylvania in 1952. … ►In 1977 Newman became a professor at the University of California, Santa Barbara, where he served until his retirement in 1993. …

23: Ingram Olkin

… … ► 2016) was Professor Emeritus of Statistics and Education in the Department of Statistics at Stanford University, California. … ► in mathematical statistics, Columbia University, New York, and Ph. … in mathematical statistics, University of North Carolina. … ►He also was a Guggenheim, Fulbright, Humboldt, and Lady Davis Fellow, had an honorary degree from De Montfort University, and was awarded the Townsend Harris Medal by the City University of New York. …

24: Foreword

… ►That 1046-page tome proved to be an invaluable reference for the many scientists and engineers who use the special functions of applied mathematics in their day-to-day work, so much so that it became the most widely distributed and most highly cited NIST publication in the first 100 years of the institution’s existence. … ►Much has changed in the years since A&S was published. Certainly, advances in applied mathematics have continued unabated. … ►The production of these new resources has been a very complex undertaking some 10 years in the making. … ►November 20, 2009 …

25: Ian J. Thompson

… ► 1953 in New Zealand) has been since 2006 a Theoretical Nuclear Physicist in the Nuclear Theory and Modeling Group of the Lawrence Livermore National Laboratory, Livermore, California. He was previously Professor in the Department of Physics, University of Surrey at Guildford, U. …at Auckland, New Zealand in 1979. ►Thompson has published papers on special functions, and numerous papers in theoretical nuclear physics, especially in scattering theory. His book Nuclear Reactions for Astrophysics was published in 2009 by Cambridge University Press. …

26: 6.20 Approximations

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§6.20(i) Approximations in Terms of Elementary Functions

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Cody and Thacher (1968) provides minimax rational approximations for $E_1\left(x\right)$, with accuracies up to 20S.

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Cody and Thacher (1969) provides minimax rational approximations for $\mathrm{Ei}\left(x\right)$, with accuracies up to 20S.

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MacLeod (1996b) provides rational approximations for the sine and cosine integrals and for the auxiliary functions $\mathrm{f}$ and $\mathrm{g}$, with accuracies up to 20S.

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§6.20(ii) Expansions in Chebyshev Series

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27: Preface

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Morris Newman, The University of California, Santa Barbara

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Ingram Olkin, Stanford University

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Peter Paule, Johannes Kepler University

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Bernard Deconinck, University of Washington

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Alexander A. Its, Indiana University

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28: Bibliography N

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Tables of Lagrangian Interpolation Coefficients. Columbia University Press, New York.

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Notes:

Technical Director: Arnold N. Lowan

External Links:

MathReview (W. Feller), ZentralBlatt

Referenced by:

§3.3(ii).

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On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.

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External Links:

ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt

Referenced by:

§28.26(ii).

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Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

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External Links:

FullText, MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

§19.37(iv).

Encodings:

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A table of integrals of the error functions. J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.

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Notes:

See for additions and corrections same journal, Sect. B 75, 149–163 (1975)

External Links:

MathReview, ZentralBlatt

Referenced by:

§7.14(iii), §7.21, §7.7(iii).

Encodings:

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Diffraction Effects in Semiclassical Scattering. Montroll Memorial Lecture Series in Mathematical Physics, Cambridge University Press.

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Notes:

Also available electronically through Cambridge Books Online, ISBN 9780511599903.

External Links:

ISBN 9780521383189, Document

Referenced by:

§9.16, §9.16.

Encodings:

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29: 7.24 Approximations

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§7.24(i) Approximations in Terms of Elementary Functions

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Cody (1969) provides minimax rational approximations for $\mathrm{erf}x$ and $\mathrm{erfc}x$. The maximum relative precision is about 20S.

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Cody et al. (1970) gives minimax rational approximations to Dawson’s integral $F\left(x\right)$ (maximum relative precision 20S–22S).

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§7.24(ii) Expansions in Chebyshev Series

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30: Bibliography R

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On the definition and properties of generalized $6$-$j$ symbols. J. Math. Phys. 20 (12), pp. 2398–2415.

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External Links:

ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§16.4(iii), §16.4(iii).

Encodings:

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High precision Chebyshev expansions for Airy functions and their derivatives. Technical report University of Birmingham Computer Centre.

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Referenced by:

3rd item.

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Universality properties of Gaussian quadrature, the derivative rule, and a novel approach to Stieltjes inversion.

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Notes:

arXiv:1812.02196

Referenced by:

§18.40(ii).

Encodings:

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Roots of $\tan x=x$ .

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Notes:

10 typewritten pages deposited in the UMT file at Lawrence Berkeley Laboratory, University of California, Berkeley, CA.

Referenced by:

§4.46.

Encodings:

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Sources in the development of mathematics. Cambridge University Press, Cambridge.

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Notes:

Infinite Series and Products from the Fifteenth to the Twenty-first Century

External Links:

ISBN 978-0-521-11470-7, Document, Link, MathReview (Mehdi Hassani), ZentralBlatt

Referenced by:

Profile Ranjan Roy.

Encodings:

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