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1: 20 Theta Functions

Chapter 20 Theta Functions

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2: 8 Incomplete Gamma and Related
Functions

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3: 28 Mathieu Functions and Hill’s Equation

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4: 23 Weierstrass Elliptic and Modular
Functions

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5: 8.26 Tables

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Khamis (1965) tabulates $P(a,x)$ for $a=0.05(.05)10(.1)20(.25)70$, $0.0001\le x\le 250$ to 10D.

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Abramowitz and Stegun (1964, pp. 245–248) tabulates $E_n\left(x\right)$ for $n=2,3,4,10,20$, $x=0(.01)2$ to 7D; also $(x+n){\mathrm{e}}^x{E}_n\left(x\right)$ for $n=2,3,4,10,20$, $x^{-1}=0(.01)0.1(.05)0.5$ to 6S.

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Pagurova (1961) tabulates $E_n\left(x\right)$ for $n=0(1)20$, $x=0(.01)2(.1)10$ to 4-9S; ${\mathrm{e}}^x{E}_n\left(x\right)$ for $n=2(1)10$, $x=10(.1)20$ to 7D; ${\mathrm{e}}^x{E}_p\left(x\right)$ for $p=0(.1)1$, $x=0.01(.01)7(.05)12(.1)20$ to 7S or 7D.

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Zhang and Jin (1996, Table 19.1) tabulates $E_n\left(x\right)$ for $n=1,2,3,5,10,15,20$, $x=0(.1)1,1.5,2,3,5,10,20,30,50,100$ to 7D or 8S.

6: Gergő Nemes

… ► 1988 in Szeged, Hungary) is a Research Fellow at the Alfréd Rényi Institute of Mathematics in Budapest, Hungary. … ► in mathematics (with distinction) and a M. …in mathematics (with honours) from Loránd Eötvös University, Budapest, Hungary and a Ph. … in mathematics from Central European University in Budapest, Hungary. … ►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions. …

7: Wolter Groenevelt

… ► 1976 in Leidschendam, the Netherlands) is an Associate Professor at the Delft University of Technology in Delft, The Netherlands. … ► in mathematics at the Delft University of Technology in 2004. ►Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems. ►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials. ►In July 2023, Groenevelt was named Contributing Developer of the NIST Digital Library of Mathematical Functions.

8: 36 Integrals with Coalescing Saddles

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9: Bibliography T

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Special functions in phase space: Mathieu functions. J. Phys. A 31 (31), pp. 6725–6739.

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External Links:

ISSN 0305-4470, Document, MathReview (Bing Hong Wang), ZentralBlatt

Referenced by:

8th item.

Encodings:

BibTeX

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Sugli zeri delle funzioni di cui si conosce una rappresentazione asintotica. Ann. Mat. Pura Appl. (4) 26, pp. 283–300 (Italian).

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External Links:

Document, MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§13.9(i).

Encodings:

BibTeX

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Sul comportamento asintotico dell’$n$-esimo polinomio di Laguerre nell’intorno dell’ascissa $4n$ . Comment. Math. Helv. 22, pp. 150–167.

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External Links:

ISSN 0010-2571, Document, MathReview (G. Szegő), ZentralBlatt

Referenced by:

§18.16(iv).

Encodings:

BibTeX

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Funzioni Ellittiche. 2nd edition, Nicola Zanichelli Editore, Bologna (Italian).

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Notes:

German edition (M. Krafft, Ed.) Akad. Verlag., Leipzig, 1948

External Links:

MathReview (Z. Nehari), ZentralBlatt

Referenced by:

Ch.19.

Encodings:

BibTeX

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On a function which occurs in the theory of the structure of polymers. Ann. of Math. (2) 46, pp. 144–157.

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External Links:

FullText, MathReview (I. Niven), ZentralBlatt

Referenced by:

§25.12(ii), Notations P.

Encodings:

BibTeX

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10: 33.24 Tables

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Abramowitz and Stegun (1964, Chapter 14) tabulates $F_0(\eta ,\rho )$, $G_0(\eta ,\rho )$, $F_0^{\prime }(\eta ,\rho )$, and $G_0^{\prime }(\eta ,\rho )$ for $\eta =0.5(.5)20$ and $\rho =1(1)20$, 5S; $C_0\left(\eta \right)$ for $\eta =0(.05)3$, 6S.

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