Theory And Applications of Special Function

by Ismail, Mourad; Rahman, Mizan; Koelink, Erik

• ISBN13: 9780387242316
• ISBN10: 0387242317
• Format: Hardcover
• Copyright: 2005-03-25
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Mizan Rahman, his Mathematics and Literary Writings	1	(28)
Richard Askey
Mourad E.H. Ismail
Erik Koelink
On the completeness of sets of q-Bessel functions Jv(3)(x;q)	29	(10)
L. D. Abreu
J. Bustoz
a-Gaussian Polynomials and Finite Rogers-Ramanujan Identities	39	(22)
George E. Andrews
On a generalized Gamma convolution related to the q-calculus	61	(16)
Christian Berg
Ramanujan and Cranks	77	(22)
Bruce C. Berndt
Heng Huat Chan
Song Heng Chan
Wen-Chin Liaw
The Saalschutz Chain Reactions and Multiple q-Series Transformations	99	(24)
CHU Wenchang
Painleve Equations and Associated Polynomials	123	(42)
Peter A. Clarkson
Zeta Functions of Heisenberg Graphs over Finite Rings	165	(20)
Michelle DeDeo
Maria Martinez
Archie Medrano
Marvin Minei
Harold Stark
Audrey Terras
q-Analogues of Some Multivariable Biorthogonal Polynomials	185	(24)
George Gasper
Mizan Rahman
Some Systems of Multivariable Orthogonal Askey-Wilson Polynomials	209	(12)
George Gasper
Mizan Rahman
Continuous Hahn functions as Clebsch-Gordan coefficients	221	(64)
Wolter Groenevelt
Erik Koelink
Hjalmar Rosengren
New Proofs of Some q-series Results	285	(16)
Mourad E.H. Ismail
Ruiming Zhang
The Little q-Jacobi Functions of Complex Order	301	(38)
Kevin W. J. Kadell
A second addition formula for continuous q-ultraspherical polynomials	339	(22)
Tom H. Koornwinder
A bilateral series involving basic hypergeometric functions	361	(6)
Hjalmar Rosengren
The Hilbert space asymptotics of a class of orthonormal polynomials on a bounded interval	367	(16)
S. N. M. Ruijsenaars
Abel-Rothe type generalizations of Jacobi's triple product identity	383	(18)
Michael Schlosser
Summable sums of hypergeometric series	401	(10)
D. Stanton
Askey-Wilson functions and quantum groups	411	(32)
Jasper V. Stokman
An Analog of the Cauchy-Hadamard Formula for Expansions in q-Polynomials	443	(18)
Sergei K. Suslov
Strong nonnegative linearization of orthogonal polynomials	461	(18)
Ryszard Szwarc
Remarks on Some Basic Hypergeometric Series	479
Changgui Zhang