Special Functions 2000: Current Perspective and Future Directions: current perspective and future directions : [proceedings of the NATO Advanced Study Institute on Special Functions 2000: Current Perspective and Future Directions, Tempe, Arizona, USA, 29 May-9 June 2000]

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Joaquin Bustoz, Mourad Ismail, Sergeĭ Konstantinovich Suslov
Springer Science & Business Media, 2001 - Mathematics - 520 pages
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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, Painleve classification.
 

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Contents

Baileys transform lemma chains and tree
1
RiemannHilbert problems for multiple orthogonal polynomials
23
Flowers which cannot yet see growing in Ramanujans garden of hypergeometric series elliptic functions and qs
61
Orthogonal rational functions and continued fractions
87
Orthogonal polynomials and reflection groups
111
an overview
129
some new perspectives
141
Lectures on qorthogonal polynomials
179
Special functions defined by analytic difference equations
281
The factorization method selfsimilar potentials and quantum algebras
335
Generalized eigenvalue problem and a new family or rational functions biorthogonal on elliptic grids
365
Orthogonal Polynomials and Combinatorics
389
Basic exponential functions on a qquadratic grid
411
Projection operator method for quantum groups
457
Uniform asymptotic expansions
489
Exponential asymptotics
505

The AskeyWilson function transform scheme
221
Arithmetic of the partition function
243
The associated classical orthogonal polynomials
255

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About the author (2001)

Mourad E. H. Ismail is Professor of Mathematics at the University of Central Florida.

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