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1: 26.19 Mathematical Applications

§26.19 Mathematical Applications

… ►Partitions and plane partitions have applications to representation theory (Bressoud (1999), Macdonald (1995), and Sagan (2001)) and to special functions (Andrews et al. (1999) and Gasper and Rahman (2004)). …

2: Wolter Groenevelt

… ►Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems. …

3: Donald St. P. Richards

… ►He is editor of the book Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications, published by the American Mathematical Society in 1992, and coeditor of Representation Theory and Harmonic Analysis: A Conference in Honor of R. A. Kunze (with T. …

4: 27.13 Functions

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§27.13(iv) Representation by Squares

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5: Bibliography T

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Representation Theory and Harmonic Analysis. Contemporary Mathematics, Vol. 191, American Mathematical Society, Providence, RI.

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Notes:

Papers from the conference held in honor of Ray A. Kunze at the AMS Special Session, Cincinnati, Ohio, January 12–14, 1994

External Links:

ISBN 0-8218-0310-7, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

Profile Donald St. P. Richards.

Encodings:

BibTeX

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6: Bibliography G

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Bessel functions and representation theory. I. J. Functional Analysis 22 (2), pp. 73–105.

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External Links:

Document, MathReview (E. A. Thieleker), ZentralBlatt

Referenced by:

§35.5(i).

Encodings:

BibTeX

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7: 18.38 Mathematical Applications

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Quadrature “Extended” to Pseudo-Spectral (DVR) Representations of Operators in One and Many Dimensions

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8: Bibliography V

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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:

BibTeX

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9: 27.4 Euler Products and Dirichlet Series

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27.4.1 $$\sum _{n=1}^{\mathrm{\infty }}f(n)=\prod _p\left(1+\sum _{r=1}^{\mathrm{\infty }}f(p^r)\right),$$

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Symbols:

$n$: positive integer, $p,p_1,\mathrm{\dots }$: prime numbers and $f$: multiplicative function

Permalink:

http://dlmf.nist.gov/27.4.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §27.4 and Ch.27

… ►Euler products are used to find series that generate many functions of multiplicative number theory. The completely multiplicative function $f(n)=n^{-s}$ gives the Euler product representation of the Riemann zeta function $\zeta \left(s\right)$ (§25.2(i)): … ►

27.4.4 $$F(s)=\sum _{n=1}^{\mathrm{\infty }}f(n)n^{-s},$$

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Symbols:

$n$: positive integer, $f$: multiplicative function and $F(s)$: generating function

Permalink:

http://dlmf.nist.gov/27.4.E4

Encodings:

pMML, png, TeX

See also:

Annotations for §27.4 and Ch.27

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10: 18.39 Applications in the Physical Sciences

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Table 18.39.1: Typical Non-Classical Weight Functions Of Use In DVR Applications^a

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Name of OP System	$w(x)$	$[a,b]$	Notation	Applications
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