Special Functions 2000: Current Perspective and Future Directions

✍ Scribed by George E. Andrews (auth.), Joaquin Bustoz, Mourad E. H. Ismail, Sergei K. Suslov (eds.)

• Publisher: Springer Netherlands
• Year: 2001
• Tongue: English
• Leaves: 520
• Series: NATO Science Series 30
• Edition: 1
• Category: Library

✦ Synopsis

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

Front Matter....Pages i-xi
Bailey’s Transform, Lemma, Chains and Tree....Pages 1-22
Riemann-Hilbert Problems for Multiple Orthogonal Polynomials....Pages 23-59
Flowers Which We Cannot Yet See Growing in Ramanujan’s Garden of Hypergeometric Series, Elliptic Functions, and q ’S....Pages 61-85
Orthogonal Rational Functions and Continued Fractions....Pages 87-109
Orthogonal Polynomials and Reflection Groups....Pages 111-128
The Bispectral Problem: An Overview....Pages 129-140
The Bochner-Krall Problem: Some New Perspectives....Pages 141-178
Lectures on q -Orthogonal Polynomials....Pages 179-219
The Askey-Wilson Function Transform Scheme....Pages 221-241
Arithmetic of the Partition Function....Pages 243-253
The Associated Classical Orthogonal Polynomials....Pages 255-279
Special Functions Defined by Analytic Difference Equations....Pages 281-333
The Factorization Method, Self-Similar Potentials and Quantum Algebras....Pages 335-364
Generalized Eigenvalue Problem and a New Family of Rational Functions Biorthogonal on Elliptic Grids....Pages 365-388
Orthogonal Polynomials and Combinatorics....Pages 389-409
Basic Exponential Functions on a q -Quadratic Grid....Pages 411-456
Projection Operator Method for Quantum Groups....Pages 457-488
Uniform Asymptotic Expansions....Pages 489-503
Exponential Asymptotics....Pages 505-518
Back Matter....Pages 519-520

✦ Subjects

Special Functions; Fourier Analysis; Group Theory and Generalizations; Combinatorics; Number Theory