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Special Functions 2000: Current Perspective and Future Directions

  • Book
  • © 2001

Overview

Editors:
  1. Joaquin Bustoz

    1. Department of Mathematics, Arizona State University, Tempe, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Mourad E. H. Ismail

    1. Department of Mathematics, University of South Florida, Tampa, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  3. Sergei K. Suslov

    1. Department of Mathematics, Arizona State University, Tempe, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry (NAII, volume 30)

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About this book

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.

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  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 NjÃ¥stad
    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
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Editors and Affiliations

  • 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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