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31: William P. Reinhardt

… ►Reinhardt is a theoretical chemist and atomic physicist, who has always been interested in orthogonal polynomials and in the analyticity properties of the functions of mathematical physics. …

32: 4.14 Definitions and Periodicity

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4.14.7 $$\cot z=\frac{\cos z}{\sin z}=\frac{1}{\tan z}.$$

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Defines:

$\cot z$: cotangent function

Symbols:

$\cos z$: cosine function, $\sin z$: sine function, $\tan z$: tangent function and $z$: complex variable

A&S Ref:

4.3.6

Referenced by:

§4.14, §4.45(i), §4.45(ii)

Permalink:

http://dlmf.nist.gov/4.14.E7

Encodings:

pMML, png, TeX

See also:

Annotations for §4.14 and Ch.4

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33: 8.17 Incomplete Beta Functions

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§8.17(i) Definitions and Basic Properties

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§8.17(vii) Addendum to 8.17(i) Definitions and Basic Properties

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34: 15.2 Definitions and Analytical Properties

§15.2 Definitions and Analytical Properties

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§15.2(ii) Analytic Properties

… ►The same properties hold for $F(a,b;c;z)$, except that as a function of $c$, $F(a,b;c;z)$ in general has poles at $c=0,-1,-2,\mathrm{\dots }$. ►Because of the analytic properties with respect to $a$, $b$, and $c$, it is usually legitimate to take limits in formulas involving functions that are undefined for certain values of the parameters. …

35: 18.19 Hahn Class: Definitions

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Hahn, Krawtchouk, Meixner, and Charlier

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Table 18.19.1: Orthogonality properties for Hahn, Krawtchouk, Meixner, and Charlier OP’s: discrete sets, weight functions, standardizations, and parameter constraints.

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	$p_n(x)$	$X$	$w_x$	$h_n$
…

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… ►A special case of (18.19.8) is $w^{(1/2)}(x;\pi /2)=\frac{\pi }{\cosh \left(\pi x\right)}$.

36: Bibliography N

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The resurgence properties of the large order asymptotics of the Anger-Weber function I. J. Class. Anal. 4 (1), pp. 1–39.

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External Links:

ISSN 1848-5979, Document, Link, MathReview (José Luis López), ZentralBlatt

Referenced by:

(11.11.10), (11.11.8), §11.11(iii).

Encodings:

BibTeX

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The resurgence properties of the large order asymptotics of the Anger-Weber function II. J. Class. Anal. 4 (2), pp. 121–147.

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External Links:

ISSN 1848-5979, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

(11.11.10), (11.11.8), §11.11(iii).

Encodings:

BibTeX

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The resurgence properties of the incomplete gamma function II. Stud. Appl. Math. 135 (1), pp. 86–116.

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External Links:

ISSN 0022-2526, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§8.11(iii).

Encodings:

BibTeX

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The resurgence properties of the incomplete gamma function, I. Anal. Appl. (Singap.) 14 (5), pp. 631–677.

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External Links:

ISSN 0219-5305, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§8.11(iii), §8.11(v), §8.11(v), Erratum (V1.0.14) for Subsections 8.18(ii)–8.11(v).

Encodings:

BibTeX

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37: 25.14 Lerch’s Transcendent

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§25.14(ii) Properties

… ►For these and further properties see Erdélyi et al. (1953a, pp. 27–31).

38: 33.14 Definitions and Basic Properties

§33.14 Definitions and Basic Properties

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§33.14(i) Coulomb Wave Equation

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§33.14(ii) Regular Solution $f(ϵ,\mathrm{\ell };r)$

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§33.14(iii) Irregular Solution $h(ϵ,\mathrm{\ell };r)$

… ►The function $s(ϵ,\mathrm{\ell };r)$ has the following properties: …

39: 7.19 Voigt Functions

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§7.19(iii) Properties

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40: 10.42 Zeros

… ►Properties of the zeros of $I_{\nu }\left(z\right)$ and $K_{\nu }\left(z\right)$ may be deduced from those of $J_{\nu }\left(z\right)$ and $H_{\nu }^{(1)}\left(z\right)$, respectively, by application of the transformations (10.27.6) and (10.27.8). …