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Theory and Applications of Special Functions: A Volume Dedicated to Mizan Rahman

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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.

Author(s): Richard Askey, Mourad E.H. Ismail (auth.), Mourad E.H. Ismail, Erik Koelink (eds.)
Series: Developments in Mathematics 13
Edition: 1
Publisher: Springer US
Year: 2005

Language: English
Pages: 491
Tags: Special Functions; Approximations and Expansions; Integral Transforms, Operational Calculus

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