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1: 8.19 Generalized Exponential Integral

§8.19 Generalized Exponential Integral

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§8.19(ii) Graphics

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§8.19(ix) Inequalities

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§8.19(x) Integrals

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§8.19(xi) Further Generalizations

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2: 16.2 Definition and Analytic Properties

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§16.2(i) Generalized Hypergeometric Series

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Polynomials

… ►Note also that any partial sum of the generalized hypergeometric series can be represented as a generalized hypergeometric function via … ►

§16.2(v) Behavior with Respect to Parameters

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3: 8.21 Generalized Sine and Cosine Integrals

§8.21 Generalized Sine and Cosine Integrals

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§8.21(i) Definitions: General Values

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§8.21(iv) Interrelations

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§8.21(v) Special Values

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4: 1.16 Distributions

… ► $\mathrm{\Lambda }:𝒟(I)\to ℂ$ is called a distribution, or generalized function, if it is a continuous linear functional on $𝒟(I)$, that is, it is a linear functional and for every ${\varphi }_n\to \varphi$ in $𝒟(I)$, … ►More generally, for $\alpha :[a,b]\to [-\mathrm{\infty },\mathrm{\infty }]$ a nondecreasing function the corresponding Lebesgue–Stieltjes measure ${\mu }_{\alpha }$ (see §1.4(v)) can be considered as a distribution: … ►More generally, if $\alpha (x)$ is an infinitely differentiable function, then … ►Friedman (1990) gives an overview of generalized functions and their relation to distributions. …

5: 35.8 Generalized Hypergeometric Functions of Matrix Argument

§35.8 Generalized Hypergeometric Functions of Matrix Argument

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§35.8(i) Definition

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Convergence Properties

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§35.8(iv) General Properties

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Confluence

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6: 19.2 Definitions

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§19.2(i) General Elliptic Integrals

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7: 29.16 Asymptotic Expansions

… ►Hargrave and Sleeman (1977) give asymptotic approximations for Lamé polynomials and their eigenvalues, including error bounds. …

8: 16.24 Physical Applications

§16.24 Physical Applications

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§16.24(i) Random Walks

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§16.24(ii) Loop Integrals in Feynman Diagrams

►Appell functions are used for the evaluation of one-loop integrals in Feynman diagrams. … ►

§16.24(iii) $\mathit{3}j$, $\mathit{6}j$, and $\mathit{9}j$ Symbols

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9: 29.19 Physical Applications

… ►Hargrave (1978) studies high frequency solutions of the delta wing equation. …

10: Bibliography H

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Lamé polynomials of large order. SIAM J. Math. Anal. 8 (5), pp. 800–842.

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External Links:

Document, MathReview (F. M. Arscott), ZentralBlatt

Referenced by:

§29.16.

Encodings:

BibTeX

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High frequency solutions of the delta wing equations. Proc. Roy. Soc. Edinburgh Sect. A 81 (3-4), pp. 299–316.

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External Links:

ISSN 0308-2105, MathReview (V. M. Babich), ZentralBlatt

Referenced by:

§29.19(ii).

Encodings:

BibTeX

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On the distribution of the zeros of generalized Airy functions. Math. Comp. 29 (131), pp. 863–877.

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External Links:

FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§9.13(i).

Encodings:

BibTeX

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