Theory and Application of Special Functions

Theory and Application of Special Functions contains the proceedings of the Advanced Seminar on Special Functions sponsored by the Mathematics Research Center of the University of Wisconsin-Madison and held from March 31 to April 2, 1975. The seminar tackled the theory and application of special functions and covered topics ranging from the asymptotic estimation of special functions to association schemes and coding theory. Some interesting results, conjectures, and problems are given.

Comprised of 13 chapters, this book begins with a survey of computational methods in special functions, followed by a discussion on unsolved problems in the asymptotic estimation of special functions. The reader is then introduced to periodic Bernoulli numbers, summation formulas, and applications; problems and prospects for basic hypergeometric functions; and linear growth models with many types and multidimensional Hahn polynomials. Subsequent chapters explore two-variable analogues of the classical orthogonal polynomials; special functions of matrix and single argument in statistics; and some properties of the determinants of orthogonal polynomials.

This monograph is intended primarily for students and practitioners of mathematics.

Foreword

Preface

Computational Methods in Special Functions-A Survey

Unsolved Problems in the Asymptotic Estimation of Special Functions

Periodic Bernoulli Numbers, Summation Formulas and Applications

Problems and Prospects for Basic Hypergeometric Functions

An Introduction to Association Schemes and Coding Theory

Linear Growth Models with Many Types and Multidimensional Hahn Polynomials

Orthogonal Polynomials Revisited

Symmetry, Separation of Variables, and Special Functions

Nicholson-Type Integrals for Products of Gegenbauer Functions and Related Topics

Positivity and Special Functions

Two-Variable Analogues of the Classical Orthogonal Polynomials

Special Functions of Matrix and Single Argument in Statistics

Some Properties of Determinants of Orthogonal Polynomials

Index