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1: 8.24 Physical Applications

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§8.24(ii) Incomplete Beta Functions

►The function $I_x(a,b)$ appears in: Monte Carlo sampling in statistical mechanics (Kofke (2004)); analysis of packings of soft or granular objects (Prellberg and Owczarek (1995)); growth formulas in cosmology (Hamilton (2001)). …

2: 26 Combinatorial Analysis

Chapter 26 Combinatorial Analysis

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3: Gergő Nemes

… ►Nemes has research interests in asymptotic analysis, Écalle theory, exact WKB analysis, and special functions. ►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions. …

4: 26.19 Mathematical Applications

… ►Combinatorics has applications to analysis, algebra, and geometry. … ►Other areas of combinatorial analysis include graph theory, coding theory, and combinatorial designs. …

5: Ira Gessel

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26 Combinatorial Analysis

6: Donald St. P. Richards

… ►Richards has published numerous papers on special functions of matrix argument, harmonic analysis, multivariate statistical analysis, probability inequalities, and applied probability. 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. …

7: Peter L. Walker

… ►Walker’s published work has been mainly in real and complex analysis, with excursions into analytic number theory and geometry, the latter in collaboration with Professor Mowaffaq Hajja of the University of Jordan. ►Walker’s books are An Introduction to Complex Analysis, published by Hilger in 1974, The Theory of Fourier Series and Integrals, published by Wiley in 1986, Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and Examples and Theorems in Analysis, published by Springer in 2004. …

8: Bibliography S

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Introductory Complex Analysis. Prentice-Hall, Inc., Englewood Cliffs, N.J..

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Notes:

Reprinted by Dover Publications Inc. 1972

External Links:

MathReview (E. Hille), ZentralBlatt

Referenced by:

Ch.4.

Encodings:

BibTeX

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Prolate spheroidal wave functions, Fourier analysis and uncertainty. I. Bell System Tech. J. 40, pp. 43–63.

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External Links:

MathReview (I. Marx), ZentralBlatt

Referenced by:

§30.15(v).

Encodings:

BibTeX

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Prolate spheroidal wave functions, Fourier analysis and uncertainity. IV. Extensions to many dimensions; generalized prolate spheroidal functions. Bell System Tech. J. 43, pp. 3009–3057.

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External Links:

ISSN 0005-8580, MathReview (J. Meixner), ZentralBlatt

Referenced by:

§30.12.

Encodings:

BibTeX

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Fourier Analysis: An Introduction. Princeton Lectures in Analysis, Vol. 1, Princeton University Press, Oxford-Princeton, NJ.

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External Links:

ISBN 0-691-11384-X, MathReview (Steven George Krantz), ZentralBlatt

Referenced by:

§5.19(iii).

Encodings:

BibTeX

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Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.

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Notes:

Sinc-Pack, a set of 480 Matlab programs with a 470-page tutorial, is available for purchase from SINC, LLC by contacting Frank Stenger.

External Links:

ISBN 0-387-94008-1, MathReview (B. Boyanov), ZentralBlatt

Referenced by:

§3.3(vi), §3.4(i), §3.5(i).

Encodings:

BibTeX

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9: Ingram Olkin

… ►Olkin’s research covered a broad range of areas, including multivariate analysis, reliability theory, matrix theory, statistical models in the social and behavioral sciences, life distributions, and meta-analysis. … Marshall), published by Academic Press in 1979, Statistical Methods for Meta-Analysis (with L. …

10: 35.9 Applications

§35.9 Applications

►In multivariate statistical analysis based on the multivariate normal distribution, the probability density functions of many random matrices are expressible in terms of generalized hypergeometric functions of matrix argument ${}_p{}^{}F_q^{}$, with $p\le 2$ and $q\le 1$. … ►For other statistical applications of ${}_p{}^{}F_q^{}$ functions of matrix argument see Perlman and Olkin (1980), Groeneboom and Truax (2000), Bhaumik and Sarkar (2002), Richards (2004) (monotonicity of power functions of multivariate statistical test criteria), Bingham et al. (1992) (Procrustes analysis), and Phillips (1986) (exact distributions of statistical test criteria). …