**Contemporary Mathematics**

Volume: 138;
1992;
259 pp;
Softcover

MSC: Primary 33;

**Print ISBN: 978-0-8218-5159-3
Product Code: CONM/138**

List Price: $60.00

AMS Member Price: $48.00

MAA Member Price: $54.00

**Electronic ISBN: 978-0-8218-7729-6
Product Code: CONM/138.E**

List Price: $56.00

AMS Member Price: $44.80

MAA Member Price: $50.40

# Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications

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*Donald St. P. Richards*

This book is the first set of proceedings to be devoted entirely to the theory of hypergeometric functions defined on domains of positivity. Most of the scientific areas in which these functions are applied include analytic number theory, combinatorics, harmonic analysis, random walks, representation theory, and mathematical physics—are represented here. This volume is based largely on lectures presented at a Special Session at the AMS meeting in Tampa, Florida in March 1991, which was devoted to hypergeometric functions of matrix argument and to fostering communication among representatives of the diverse scientific areas in which these functions are utilized. Accessible to graduate students and others seeking an introduction to the state of the art in this area, this book is a suitable text for advanced graduate seminar courses for it contains many open problems.

#### Readership

Mathematicians, mathematical physicists, mathematical statisticians and graduate students seeking an introduction to the literature.

# Table of Contents

## Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications

- Contents v6 free
- Preface vii8 free
- Special functions on finite upper half planes 112 free
- Some special values for the BC type hypergeometric function 2738
- On certain spaces of harmonic polynomials 5162
- Identities for generalized hypergeometric coefficients 8798
- Eigen analysis for some examples of the Metropolis algorithm 99110
- Hilbert spaces of vector-valued holomorphic functions and irreducibility of multiplier representations 119130
- Hankel transforms associated to finite reflection groups 123134
- Prolongement analytique des series de Taylor spheriques 139150
- Some combinatorial aspects of the spectra of normally distributed random matrices 151162
- Degenerate principle series on tube type domains 175186
- Askey-Wilson polynomials for root systems of type BC 189200
- Some special functions in the Fock space 205216
- Matrice de Hua et polynomes de Jack 223234
- Generalized hypergeometric functions and Laguerre polynomials in two variables 239250