Theory and Application of Special Functions : Proceedings of an Advanced Seminar Sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31-April 2, 1975

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. Content: Front Matter, Page iii Copyright, Page iv Foreword, Page vii Preface, Pages ix-xi Computational Methods in Special Functions-A Survey, Pages 1-98, Walter Gautschi Unsolved Problems in the Asymptotic Estimation of Special Functions, Pages 99-142, F.W.J. Olver Periodic Bernoulli Numbers, Summation Formulas and Applications, Pages 143-189, Bruce C. Berndt Problems and Prospects for Basic Hypergeometric Functions, Pages 191-224, George E. Andrews An Introduction to Association Schemes and Coding Theory, Pages 225-260, N.J.A. Sloane Linear Growth Models with Many Types and Multidimensional Hahn Polynomials, Pages 261-288, S. Karlin, J. McGregor Orthogonal Polynomials Revisited, Pages 289-304, K.M. Case Symmetry, Separation of Variables, and Special Functions, Pages 305-351, Willard Miller Jr. Nicholson-Type Integrals for Products of Gegenbauer Functions and Related Topics, Pages 353-374, L. Durand Positivity and Special Functions, Pages 375-433, George Gasper Two-Variable Analogues of the Classical Orthogonal Polynomials, Pages 435-495, Tom Koornwinder Special Functions of Matrix and Single Argument in Statistics, Pages 497-520, Alan T. James Some Properties of Determinants of Orthogonal Polynomials, Pages 521-550, Samuel Karlin, James McGregor Index, Pages 551-560 Edited By Richard A. Askey. Includes Bibliographies And Index.