Theory and Applications of Special Functions: A Volume Dedicated to Mizan Rahman (Developments in Mathematics (13))

This book, dedicated to Mizan Rahman, is made up of a collection of articles on various aspects of q-series and special functions. Also, it includes an article by Askey, Ismail, and Koelink on Rahman’s mathematical contributions and how they influenced the recent upsurge in the subject. __Audience__ This book is intended for researchers and graduate students in special functions, algebraic combinatorics, quantum groups, and integrable systems. Mizan Rahman, His Mathematics and Literary Writings....Pages 1-28 a -Gaussian Polynomials and Finite Rogers-Ramanujan Identities....Pages 29-38 On a Generalized Gamma Convolution Related to the q -Calculus....Pages 39-60 Ramanujan and Cranks....Pages 61-76 The Saalschütz Chain Reactions and Multiple q -Series Transformations....Pages 77-98 Painlevé Equations and Associated Polynomials....Pages 99-121 Zeta Functions of Heisenberg Graphs over Finite Rings....Pages 123-163 q -Analogues of Some Multivariable Biorthogonal Polynomials....Pages 165-183 Some Systems of Multivariable Orthogonal Askey-Wilson Polynomials....Pages 185-208 Continuous Hahn Functions as Clebsch-Gordan Coefficients....Pages 209-219 New Proofs of Some q -Series Results....Pages 221-284 The Little q -Jacobi Functions of Complex Order....Pages 285-299 A Second Addition Formula for Continuous q -Ultraspherical Polynomials....Pages 301-338 A Bilateral Series Involving Basic Hypergeometric Functions....Pages 339-360 The Hilbert Space Asymptotics of a Class of Orthonormal Polynomials on a Bounded Interval....Pages 361-366 Abel-Rothe Type Generalizations of Jacobi's Triple Product Identity....Pages 367-381 Summable Sums of Hypergeometric Series....Pages 383-400 Askey-Wilson Functions and Quantum Groups....Pages 401-410 An Analog of the Cauchy-Hadamard Formula for Expansions in q -Polynomials....Pages 411-442 Strong Nonnegative Linearization of Orthogonal Polynomials....Pages 443-460 Remarks on Some Basic Hypergeometric Series....Pages 461-477 ....Pages 479-491 This volume,'Theory and Applications of Special Functions,'is d- icated to Mizan Rahman in honoring him for the many important c- tributions to the theory of special functions that he has made over the years, and still continues to make. Some of the papers were presented at a special session of the American Mathematical Society Annual Meeting in Baltimore, Maryland, in January 2003 organized by Mourad Ismail. Mizan Rahman's contributions are not only contained in his own - pers, but also indirectly in other papers for which he supplied useful and often essential information. We refer to the paper on his mathematics in this volume for more information. This paper contains some personal recollections and tries to describe Mizan Rahman's literary writings in his mother tongue, Bengali. An even more personal paper on Mizan Rahman is the letter by his sons, whom we thank for allowing us to reproduce it in this book. The theory of special functions is very much an application driven field of mathematics. This is a very old field, dating back to the 18th century when physicists and mathematician were looking for solutions of the fundamental differential equations of mathematical physics. Since then the field has grown enormously, and this book reflects only part of the known applications. "This book, dedicated to Mizan Rahman, is made up of a collection of articles on various aspects of q-series and special functions. It also includes an article by Askey, Ismail, and Koelink on Rahman's mathematical contributions and how they influenced the recent upsurge in the subject." "Theory and Applications of Special Functions is intended for researchers and graduate students in special functions, algebraic combinatorics, quantum groups, and integrable systems."--BOOK JACKET Edited By Mourad E.h. Ismail, Erik Koelink. Bibliography Of Mizan Rahman (p. 11-21). Includes Bibliographical References.