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1: 28.12 Definitions and Basic Properties

… ►The introduction to the eigenvalues and the functions of general order proceeds as in §§28.2(i), 28.2(ii), and 28.2(iii), except that we now restrict $\widehat{\nu }\ne 0,1$; equivalently $\nu \ne n$. … ►

§28.12(ii) Eigenfunctions ${\mathrm{me}}_{\nu }(z,q)$

… ►For $q=0$, … ► … ►

2: 28.2 Definitions and Basic Properties

… ►The general solution of (28.2.16) is $\nu =\pm \widehat{\nu }+2n$, where $n\in \mathbb{Z}$. … ►

§28.2(vi) Eigenfunctions

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3: 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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4: 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(xi) Further Generalizations

►For higher-order generalized exponential integrals see Meijer and Baken (1987) and Milgram (1985).

5: 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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6: 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 … ►Suppose $f(x)$ is infinitely differentiable except at $x_0$, where left and right derivatives of all orders exist, and … ►Friedman (1990) gives an overview of generalized functions and their relation to distributions. …

7: 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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8: 19.2 Definitions

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§19.2(i) General Elliptic Integrals

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9: Bibliography D

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Detection of the density matrix through optical homodyne tomography without filtered back projection. Phys. Rev. A 50 (5), pp. 4298–4302.

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Referenced by:

§13.28(iii).

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A simplified algorithm for the second-order sound fields. J. Acoust. Soc. Amer. 108 (6), pp. 2759–2764.

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Document

Referenced by:

§8.24(iii).

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Uniform asymptotic expansions for associated Legendre functions of large order. Proc. Roy. Soc. Edinburgh Sect. A 133 (4), pp. 807–827.

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External Links:

ISSN 0308-2105, Document, MathReview, ZentralBlatt

Referenced by:

§14.15(i), §14.15(i), §14.15(ii), §14.15(ii), §14.26.

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Conical functions of purely imaginary order and argument. Proc. Roy. Soc. Edinburgh Sect. A 143 (5), pp. 929–955.

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External Links:

ISSN 0308-2105, Document, Link, MathReview (Eugenia N. Petropoulou), ZentralBlatt

Referenced by:

§14.20(ix), §14.20(ix).

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A survey on orthogonal matrix polynomials satisfying second order differential equations. J. Comput. Appl. Math. 178 (1-2), pp. 169–190.

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External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§18.36(iv).

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10: Bibliography C

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An algorithm for exponential integrals of real order. Computing 45 (3), pp. 269–276.

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Notes:

Includes Fortran code

External Links:

ISSN 0010-485X, Document, MathReview, ZentralBlatt

Referenced by:

§8.25(v), §8.28(vi).

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Optimized fast Hankel transform filters. Geophysical Prospecting 38 (5), pp. 545–568.

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Referenced by:

§10.74(vii).

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The zeros of Hankel functions as functions of their order. Numer. Math. 7 (3), pp. 238–250.

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ISSN 0029-599X, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(xiv).

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Zeros of the Hankel function of real order out of the principal Riemann sheet. J. Comput. Appl. Math. 37 (1-3), pp. 89–99.

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ISSN 0377-0427, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.21(ix).

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Zeros of the Hankel function of real order and of its derivative. Math. Comp. 39 (160), pp. 639–645.

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External Links:

ISSN 0025-5718, FullText, MathReview (S. Ahmed), ZentralBlatt

Referenced by:

§10.21(ix).

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