Special Functions 2000 : Current Perspective and Future Directions: Proceedings of the NATO Advanced Study Institute Special Functions 2000, Arizona State University, Tempe, USA, May 29 to June 9, 2000

by NATO Advanced Study Institute Special Functions 2000 (2000 : Tempe, Ariz.); Ismail, Mourad E. H.; Suslov, Sergei K.; Bustoz, Joaquin; Bustoz, Joaquin; Ismail, Mourad E. H.; Suslov, Sergei K.

• ISBN13: 9780792371199
• ISBN10: 0792371194
• Format: Hardcover
• Copyright: 2001-09-01
• Publisher: Kluwer Academic Pub

Summary

The Advanced Study Institute brought together researchers in the main areas of special functions and applications to present recent developments in the theory, review the accomplishments of past decades, and chart directions for future research. Some of the topics covered are orthogonal polynomials and special functions in one and several variables, asymptotic, continued fractions, applications to number theory, combinatorics and mathematical physics, integrable systems, harmonic analysis and quantum groups, Painlevé classification.

Table of Contents

Preface	vii
Foreword	ix
Bailey's transform, lemma, chains and tree	1	(22)
George E. Andrews
Riemann-Hilbert problems for multiple orthogonal polynomials	23	(38)
Walter Van Assche
Jeffrey S. Geronimo
Arno B. J. Kuijlaars
Flowers which we cannot yet see growing in Ramanujan's garden of hypergeometric series, elliptic functions and q's	61	(26)
Bruce C. Berndt
Orthogonal rational functions and continued fractions	87	(24)
Adhemar Bultheel
Pablo Gonzalez-Vera
Erik Hendriksen
Olav Njastad
Orthogonal polynomials and reflection groups	111	(18)
Charles F. Dunkl
The bispectral problem: an overview	129	(12)
F. Alberto Grünbaum
The Bochner-Krall problem: some new perspectives	141	(38)
Luc Haine
Lectures on q-orthogonal polynomials	179	(42)
Mourad E. H. Ismail
The Askey-Wilson function transform scheme	221	(22)
Erik Koelink
Jasper V. Stokman
Arithmetic of the partition function	243	(12)
Ken Ono
The associated classical orthogonal polynomials	255	(26)
Mizan Rahman
Special functions defined by analytic difference equations	281	(54)
S. N. M. Ruijsenaars
The factorization method, self-similar potentials and quantum algebras	335	(30)
V. P. Spiridonov
Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids	365	(24)
V. P. Spiridonov
A. S. Zhedanov
Orthogonal polynomials and combinatorics	389	(22)
Dennis Stanton
Basic exponential functions on a q-quadratic grid	411	(46)
Sergei K. Suslov
Projection operator method for quantum groups	457	(32)
V. N. Tolstoy
Uniform asymptotic expansions	489	(16)
R. Wong
Exponential asymptotics	505	(14)
R. Wong
Index	519