Special Functions 2000: Current Perspective and Future Directions

1. Front Matter

   Pages i-xi

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2. Bailey’s Transform, Lemma, Chains and Tree

   • George E. Andrews

   Pages 1-22

3. Riemann-Hilbert Problems for Multiple Orthogonal Polynomials

   • Walter Van Assche, Jeffrey S. Geronimo, Arno B. J. Kuijlaars

   Pages 23-59

4. Flowers Which We Cannot Yet See Growing in Ramanujan’s Garden of Hypergeometric Series, Elliptic Functions, and q’S

   • Bruce C. Berndt

   Pages 61-85

5. Orthogonal Rational Functions and Continued Fractions

   • Adhemar Bultheel, Pablo Gonzalez-Vera, Erik Hendriksen, Olav Njåstad

   Pages 87-109

6. Orthogonal Polynomials and Reflection Groups

   • Charles F. Dunkl

   Pages 111-128

7. The Bispectral Problem: An Overview

   • F. Alberto Grunbaum

   Pages 129-140

8. The Bochner-Krall Problem: Some New Perspectives

   • Luc Haine

   Pages 141-178

9. Lectures on q-Orthogonal Polynomials

   • Mourad E. H. Ismail

   Pages 179-219

10. The Askey-Wilson Function Transform Scheme

    • Erik Koelink, Jasper V. Stokman

    Pages 221-241

11. Arithmetic of the Partition Function

    • Ken Ono

    Pages 243-253

12. The Associated Classical Orthogonal Polynomials

    • Mizan Rahman

    Pages 255-279

13. Special Functions Defined by Analytic Difference Equations

    • S. N. M. Ruijsenaars

    Pages 281-333

14. The Factorization Method, Self-Similar Potentials and Quantum Algebras

    • V. P. Spiridonov

    Pages 335-364

15. Generalized Eigenvalue Problem and a New Family of Rational Functions Biorthogonal on Elliptic Grids

    • V. P. Spiridonov, A. S. Zhedanov

    Pages 365-388

16. Orthogonal Polynomials and Combinatorics

    • Dennis Stanton

    Pages 389-409

17. Basic Exponential Functions on a q-Quadratic Grid

    • Sergei K. Suslov

    Pages 411-456

18. Projection Operator Method for Quantum Groups

    • V. N. Tolstoy

    Pages 457-488

19. Uniform Asymptotic Expansions

    • R. Wong

    Pages 489-503

20. Exponential Asymptotics

    • R. Wong

    Pages 505-518

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.

• Combinatorics
• Partition
• classification
• harmonic analysis
• number theory

• Department of Mathematics, Arizona State University, Tempe, USA

  Joaquin Bustoz, Sergei K. Suslov

• Department of Mathematics, University of South Florida, Tampa, USA

  Mourad E. H. Ismail

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