S. V. Aksenov, M. A. Savageau, U. D. Jentschura, J. Becher, G. Soff, and P. J. Mohr (2003) Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics. Comput. Phys. Comm. 150 (1), pp. 1–20.

ⓘ

Notes:: Includes algorithms for Lerch’s transcendent. C and Mathematica codes by Aksenov and Jentschura are available.
External Links:: Code, Document
Referenced by:: 1st item.
Encodings:: BibTeX

… ►

D. E. Amos (1989) Repeated integrals and derivatives of

K

Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.

ⓘ

External Links:: ISSN 0036-1410, Document, MathReview (A. Haimovici), ZentralBlatt
Referenced by:: §10.43(iii).
Encodings:: BibTeX

… ►

R. Askey and B. Razban (1972) An integral for Jacobi polynomials. Simon Stevin 46, pp. 165–169.

ⓘ

External Links:: MathReview (H. M. Srivastava), ZentralBlatt
Referenced by:: §18.17(viii).
Encodings:: BibTeX

…

25: 8.26 Tables

… ►

•

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

… ►

•

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 $(x+n)e^{x}E_{n}\left(x\right)$ for $n=2,3,4,10,20$ , $x^{-1}=0(.01)0.1(.05)0.5$ to 6S.

… ►

•

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

… ►

•

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.

26: 23 Weierstrass Elliptic and Modular
Functions

…

27: 22.21 Tables

§22.21 Tables

►Spenceley and Spenceley (1947) tabulates

\operatorname{sn}\left(Kx,k\right)

\operatorname{cn}\left(Kx,k\right)

\operatorname{dn}\left(Kx,k\right)

\operatorname{am}\left(Kx,k\right)

\mathcal{E}\left(Kx,k\right)

for

\operatorname{arcsin}k=1^{\circ}(1^{\circ})89^{\circ}

and

x=0\left(\tfrac{1}{90}\right)1

to 12D, or 12 decimals of a radian in the case of

\operatorname{am}\left(Kx,k\right)

. … ►Lawden (1989, pp. 280–284 and 293–297) tabulates

\operatorname{sn}\left(x,k\right)

\operatorname{cn}\left(x,k\right)

\operatorname{dn}\left(x,k\right)

\mathcal{E}\left(x,k\right)

\mathrm{Z}\left(x|k\right)

to 5D for

k=0.1(.1)0.9

x=0(.1)X

, where

X

ranges from 1. … ►Zhang and Jin (1996, p. 678) tabulates

\operatorname{sn}\left(Kx,k\right)

\operatorname{cn}\left(Kx,k\right)

\operatorname{dn}\left(Kx,k\right)

for

k=\frac{1}{4},\frac{1}{2}

and

x=0(.1)4

to 7D. …

28: 18.5 Explicit Representations

… ►

§18.5(iii) Finite Power Series, the Hypergeometric Function, and Generalized Hypergeometric Functions

… ►

Jacobi

… ►For corresponding formulas for Chebyshev, Legendre, and the Hermite

\mathit{He}_{n}

polynomials apply (18.7.3)–(18.7.6), (18.7.9), and (18.7.11). … ►The first of each of equations (18.5.7) and (18.5.8) can be regarded as definitions of

P^{(\alpha,\beta)}_{n}\left(x\right)

when the conditions

\alpha>-1

and

\beta>-1

are not satisfied. …For this reason, and also in the interest of simplicity, in the case of the Jacobi polynomials

P^{(\alpha,\beta)}_{n}\left(x\right)

we assume throughout this chapter that

\alpha>-1

and

\beta>-1

, unless stated otherwise. …

29: 27.1 Special Notation

… ► ►►►►►

$d, k, m, n$	positive integers (unless otherwise indicated).
…
$\sum_{d\mathbin{\|}n}$ , $\prod_{d\mathbin{\|}n}$	sum, product taken over divisors of $n$ .
…
$\sum_{p}$ , $\prod_{p}$	sum, product extended over all primes.
…
$(n\|P)$	Jacobi symbol; see §27.9.
…

30: 17.8 Special Cases of ${{}_{r}\psi_{r}}$ Functions

… ►

Jacobi’s Triple Product

… ►

Quintuple Product Identity

…

Jacobi%20triple%20product

21—30 of 333 matching pages

21: 8 Incomplete Gamma and Related Functions

22: 28 Mathieu Functions and Hill’s Equation

23: 18.1 Notation

Classical OP’s

24: Bibliography