Rayleigh function

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1: 10.73 Physical Applications

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§10.73(v) Rayleigh Function

►For applications of the Rayleigh function ${\sigma }_n\left(\nu \right)$ (§10.21(xiii)) to problems of heat conduction and diffusion in liquids see Kapitsa (1951a).

2: 10.21 Zeros

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§10.21(xiii) Rayleigh Function

►The Rayleigh function ${\sigma }_n\left(\nu \right)$ is defined by ►

10.21.55 $${\sigma }_n\left(\nu \right)=\sum _{m=1}^{\mathrm{\infty }}{(j_{\nu ,m})}^{-2n},$$ $n=1,2,3,\mathrm{\dots }$.

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Defines:

${\sigma }_n\left(\nu \right)$: Rayleigh function

Symbols:

$m$: integer, $n$: integer and $\nu$: complex parameter

Permalink:

http://dlmf.nist.gov/10.21.E55

Encodings:

pMML, png, TeX

See also:

Annotations for §10.21(xiii), §10.21 and Ch.10

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3: 10.49 Explicit Formulas

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§10.49(iii) Rayleigh’s Formulas

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4: Bibliography K

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The Rayleigh function: Theory and computational methods. Zh. Vychisl. Mat. Mat. Fiz. 39 (12), pp. 1962–2006.

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Notes:

Translation in Comput. Math. Math. Phys. 39 (1999), No. 12, pp. 1883–1925.

External Links:

ISSN 0044-4669, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.21(xiii).

Encodings:

BibTeX

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Overview of some new results concerning the theory and applications of the Rayleigh special function. Comput. Math. Math. Phys. 48 (9), pp. 1454–1507.

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External Links:

ISSN 0965-5425, Document, FullText

Referenced by:

§10.21(xiii), §10.21(xiii).

Encodings:

BibTeX

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5: Bibliography G

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Riccati equations and convolution formulae for functions of Rayleigh type. J. Phys. A 33 (7), pp. 1363–1368.

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External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§10.21(xiii).

Encodings:

BibTeX

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6: Bibliography V

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Calculation of Special Functions: The Gamma Function, the Exponential Integrals and Error-Like Functions. CWI Tract, Vol. 10, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam.

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Notes:

A reprint was published in 1986.

External Links:

ISBN 90-6196-277-3, MathReview (John P. Coleman), ZentralBlatt

Referenced by:

§5.21, §6.18(iv), §7.22(v), §7.6(i), §7.7(i), §7.7(ii).

Encodings:

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An infinite series of Weber’s parabolic cylinder functions. Proc. Benares Math. Soc. (N.S.) 3, pp. 37.

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External Links:

MathReview (M. C. Gray), ZentralBlatt

Referenced by:

§12.13(ii).

Encodings:

BibTeX

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Transformations of some Gauss hypergeometric functions. J. Comput. Appl. Math. 178 (1-2), pp. 473–487.

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External Links:

ISSN 0377-0427, Document, Link, MathReview (Wolfgang Bühring), ZentralBlatt

Referenced by:

§15.8(v).

Encodings:

BibTeX

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Special Functions and the Theory of Group Representations. American Mathematical Society, Providence, RI.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§13.27.

Encodings:

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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation. Constr. Approx. 20 (1), pp. 39–54.

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External Links:

ISSN 0176-4276, Document, MathReview, ZentralBlatt

Referenced by:

§30.16(i), §30.16(ii), §30.16(ii).

Encodings:

BibTeX

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7: Bibliography L

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Further inequalities for the gamma function. Math. Comp. 42 (166), pp. 597–600.

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External Links:

ISSN 0025-5718, FullText, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§5.6(i).

Encodings:

BibTeX

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Monotonicity of the differences of zeros of Bessel functions as a function of order. Proc. Amer. Math. Soc. 15 (1), pp. 91–96.

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External Links:

ISSN 0002-9939, FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(ii).

Encodings:

BibTeX

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The Theory of Sound. 2nd edition, Dover Publications, New York.

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Notes:

Photographic reproduction of the 1929 reprint of the edition of 1894–1896, published by Macmillan, London.

External Links:

MathReview, ZentralBlatt

Referenced by:

§10.73(i).

Encodings:

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Integral representation of the Hankel function in terms of parabolic cylinder functions. Quart. J. Mech. Appl. Math. 23 (3), pp. 315–327.

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External Links:

Document, MathReview (T. Erber), ZentralBlatt

Referenced by:

§12.12, §12.16.

Encodings:

BibTeX

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Expansion of the confluent hypergeometric function in series of Bessel functions. Math. Tables Aids Comput. 13 (68), pp. 261–271.

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External Links:

FullText, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§13.24(ii).

Encodings:

BibTeX

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