Theory and Applications of Special Functions

1. Front Matter

   Pages i-xii

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2. Mizan Rahman, His Mathematics and Literary Writings

   • Richard Askey, Mourad E.H. Ismail, Erik Koelink

   Pages 1-28

3. On the Completeness of Sets of q-Bessel Functions J ⁽³⁾_ν (x; q)

   • L. D. Abreu, J. Bustoz

   Pages 29-38

4. a-Gaussian Polynomials and Finite Rogers-Ramanujan Identities

   • George E. Andrews

   Pages 39-60

5. On a Generalized Gamma Convolution Related to the q-Calculus

   • Christian Berg

   Pages 61-76

6. Ramanujan and Cranks

   • Bruce C. Berndt, Heng Huat Chant, Song Heng Chan, Wen-Chin Liawt

   Pages 77-98

7. The Saalschütz Chain Reactions and Multiple q-Series Transformations

   • C H U Wenchang

   Pages 99-121

8. Painlevé Equations and Associated Polynomials

   • Peter A. Clarkson

   Pages 123-163

9. Zeta Functions of Heisenberg Graphs over Finite Rings

   • Michelle DeDeo, María Martínez, Archie Medrano, Marvin Minei, Harold Stark, Audrey Terras

   Pages 165-183

10. q-Analogues of Some Multivariable Biorthogonal Polynomials

    • George Gasper, Mizan Rahman

    Pages 185-208

11. Some Systems of Multivariable Orthogonal Askey-Wilson Polynomials

    • George Gasper, Mizan Rahman

    Pages 209-219

12. Continuous Hahn Functions as Clebsch-Gordan Coefficients

    • Wolter Groenevelt, Erik Koelink, Hjalmar Rosengren

    Pages 221-284

13. New Proofs of Some q-Series Results

    • Mourad E.H. Ismail, Ruiming Zhang

    Pages 285-299

14. The Little q-Jacobi Functions of Complex Order

    • Kevin W. J. Kadell

    Pages 301-338

15. A Second Addition Formula for Continuous q-Ultraspherical Polynomials

    • Tom H. Koornwinder

    Pages 339-360

16. A Bilateral Series Involving Basic Hypergeometric Functions

    • Hjalmar Rosengren

    Pages 361-366

17. The Hilbert Space Asymptotics of a Class of Orthonormal Polynomials on a Bounded Interval

    • S. N. M. Ruijsenaars

    Pages 367-381

18. Abel-Rothe Type Generalizations of Jacobi's Triple Product Identity

    • Michael Schlosser

    Pages 383-400

19. Summable Sums of Hypergeometric Series

    • D. Stanton

    Pages 401-410

20. Askey-Wilson Functions and Quantum Groups

    • Jasper V. Stokman

    Pages 411-442

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.

• Finite
• Hilbert space
• Hypergeometric function
• Identity
• convolution
• equation
• function
• mathematics
• orthogonal polynomials
• proof
• variable

From the reviews:

"This is a collection of papers dedicated to Mizan Rahman, who is best known in the mathematical community for co-authoring with George Gasper the modern classic Basic Hypergeometric Series … . There is also a valuable survey of Rahman’s work by the editors … . many world leaders in special functions have contributed, and the overall quality is very high. Anyone working in q-series should own this collection. It may also be of interest to people in other areas within or related to special functions." (Warren Johnson, MathDL, May, 2005)

• University of Central Florida, USA

  Mourad E.H. Ismail

• Technische Universiteit Delft, The Netherlands

  Erik Koelink

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