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11: William P. Reinhardt

… ►Reinhardt was elected to Fellowship in: The American Physical Society 1980, the American Association for the Advancement of Science 1983, Phi Beta Kappa 1998, and The Institute of Physics (UK) 2000. … ►

20 Theta Functions

… ►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.

12: 27.15 Chinese Remainder Theorem

… ►Their product

m

has 20 digits, twice the number of digits in the data. …These numbers, in turn, are combined by the Chinese remainder theorem to obtain the final result

\pmod{m}

, which is correct to 20 digits. …

13: Peter L. Walker

… ►Walker is now retired and living in Cheltenham, UK. … ►

20 Theta Functions

…

14: 6.19 Tables

… ►

•

Zhang and Jin (1996, pp. 652, 689) includes $\operatorname{Si}\left(x\right)$ , $\operatorname{Ci}\left(x\right)$ , $x=0(.5)20(2)30$ , 8D; $\operatorname{Ei}\left(x\right)$ , $E_{1}\left(x\right)$ , $x=[0,100]$ , 8S.

… ►

•

Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of $ze^{z}E_{1}\left(z\right)$ , $x=-19(1)20$ , $y=0(1)20$ , 6D; $e^{z}E_{1}\left(z\right)$ , $x=-4(.5)-2$ , $y=0(.2)1$ , 6D; $E_{1}\left(z\right)+\ln z$ , $x=-2(.5)2.5$ , $y=0(.2)1$ , 6D.

►

•

Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of $E_{1}\left(z\right)$ , $\pm x=0.5,1,3,5,10,15,20,50,100$ , $y=0(.5)1(1)5(5)30,50,100$ , 8S.

15: Staff

… ►

William P. Reinhardt, University of Washington, Chaps. 20, 22, 23

… ►

Peter L. Walker, American University of Sharjah, Chaps. 20, 22, 23

… ►

William P. Reinhardt, University of Washington, for Chaps. 20, 22, 23

… ►

Peter L. Walker, American University of Sharjah, for Chaps. 20, 22, 23

…

16: Bibliography N

… ►

D. Naylor (1989) On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.

ⓘ

External Links:: ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt
Referenced by:: §28.26(ii).
Encodings:: BibTeX

… ►

W. J. Nellis and B. C. Carlson (1966) Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

ⓘ

External Links:: FullText, MathReview (I. A. Stegun), ZentralBlatt
Referenced by:: §19.37(iv).
Encodings:: BibTeX

… ►

E. W. Ng and M. Geller (1969) A table of integrals of the error functions. J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.

ⓘ

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:: BibTeX

… ►

H. M. Nussenzveig (1992) Diffraction Effects in Semiclassical Scattering. Montroll Memorial Lecture Series in Mathematical Physics, Cambridge University Press.

ⓘ

Notes:: Also available electronically through Cambridge Books Online, ISBN 9780511599903.
External Links:: ISBN 9780521383189, Document
Referenced by:: §9.16, §9.16.
Encodings:: BibTeX

…

17: 10.75 Tables

… ►

•

Achenbach (1986) tabulates $J_{0}\left(x\right)$ , $J_{1}\left(x\right)$ , $Y_{0}\left(x\right)$ , $Y_{1}\left(x\right)$ , $x=0(.1)8$ , 20D or 18–20S.

… ►

•

Bickley et al. (1952) tabulates $x^{-n}I_{n}\left(x\right)$ or $e^{-x}I_{n}\left(x\right)$ , $x^{n}K_{n}\left(x\right)$ or $e^{x}K_{n}\left(x\right)$ , $n=2(1)20$ , $x=0$ (.01 or .1) 10(.1) 20, 8S; $I_{n}\left(x\right)$ , $K_{n}\left(x\right)$ , $n=0(1)20$ , $x=0$ or $0.1(.1)20$ , 10S.

… ►

•

Kerimov and Skorokhodov (1984b) tabulates all zeros of the principal values of $K_{n}\left(z\right)$ and $K_{n}'\left(z\right)$ , for $n=2(1)20$ , 9S.

… ►

•

Zhang and Jin (1996, p. 322) tabulates $\operatorname{ber}x$ , $\operatorname{ber}'x$ , $\operatorname{bei}x$ , $\operatorname{bei}'x$ , $\operatorname{ker}x$ , $\operatorname{ker}'x$ , $\operatorname{kei}x$ , $\operatorname{kei}'x$ , $x=0(1)20$ , 7S.

… ►

•

Zhang and Jin (1996, p. 323) tabulates the first $20$ real zeros of $\operatorname{ber}x$ , $\operatorname{ber}'x$ , $\operatorname{bei}x$ , $\operatorname{bei}'x$ , $\operatorname{ker}x$ , $\operatorname{ker}'x$ , $\operatorname{kei}x$ , $\operatorname{kei}'x$ , 8D.

18: 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. …

19: 6.20 Approximations

… ►

•

Cody and Thacher (1968) provides minimax rational approximations for $E_{1}\left(x\right)$ , with accuracies up to 20S.

►

•

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

►

•

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.

…

20: 13.30 Tables

… ►

•

Zhang and Jin (1996, pp. 411–423) tabulates $M\left(a,b,x\right)$ and $U\left(a,b,x\right)$ for $a=-5(.5)5$ , $b=0.5(.5)5$ , and $x=0.1,1,5,10,20,30$ , 8S (for $M\left(a,b,x\right)$ ) and 7S (for $U\left(a,b,x\right)$ ).

…