Contemporary Mathematics 1992; 259 pp; softcover Volume: 138 ISBN10: 0821851594 ISBN13: 9780821851593 List Price: US$56 Member Price: US$44.80 Order Code: CONM/138
 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 physicsare 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  J. Angel, N. Celniker, S. Poulos, A. Terras, C. Trimble, and E. Velasquez  Special functions on finite upper half planes
 R. J. Beerends  Some special values for the \(BC\) type hypergeometric function
 N. Bergeron and A. M. Garsia  On certain spaces of harmonic polynomials
 L. C. Biedenharn and J. D. Louck  Identities for generalized hypergeometric coefficients
 P. Diaconis and P. Hanlon  Eigen analysis for some examples of the Metropolis algorithm
 H. Ding  Hilbert spaces of vectorvalued holomorphic functions and irreducibility of multiplier representations
 C. F. Dunkl  Hankel transforms associated to finite reflection groups
 J. Faraut  Prolongement analytique des series de Taylor spheriques
 P. J. Hanlon, R. P. Stanley, and J. R. Stembridge  Some combinatorial aspects of the spectra of normally distributed random matrices
 K. D. Johnson  Degenerate principle series on tube type domains
 T. H. Koornwinder  AskeyWilson polynomials for root systems of type \(BC\)
 R. A. Kunze  Some special functions in the Fock space
 M. Lassalle  Matrice de Hua et polynômes de Jack
 Z. Yan  Generalized hypergeometric functions and Laguerre polynomials in two variables
