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Encyclopedia of Special Functions: The Askey-Bateman Project

Volume 2. Multivariable Special Functions

$79.99 (C)

Tom H. Koornwinder, Jasper V. Stokman, Yuan Xu, Keiji Matsumoto, Nobuki Takayama, Michael J. Schlosser, Hjalmar Rosengren, S. Ole Warnaar, Charles F. Dunkl, Gert J. Heckman, Eric M. Opdam, Jim Haglund, Vitaly Tarasov, Alexander Varchenko, Joris Van der Jeugt
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  • Date Published: November 2020
  • availability: In stock
  • format: Hardback
  • isbn: 9781107003736


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About the Authors
  • This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.

    • A necessary update of the Bateman Manuscript Project for the twenty-first century
    • Gives an encyclopedic survey of multivariable special functions, providing an excellent starting point for readers who need guidance to the scattered literature
    • Emphasizes the connections between multivariable special functions and other fields, in particular, Lie theory and mathematical physics
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    Product details

    • Date Published: November 2020
    • format: Hardback
    • isbn: 9781107003736
    • length: 434 pages
    • dimensions: 251 x 175 x 28 mm
    • weight: 0.89kg
    • contains: 17 b/w illus. 6 tables
    • availability: In stock
  • Table of Contents

    1. General overview of multivariable special functions Tom H. Koornwinder and Jasper V. Stokman
    2. Orthogonal polynomials of several variables Yuan Xu
    3. Appell and Lauricella hypergeometric functions Keiji Matsumoto
    4. A-Hypergeometric functions Nobuki Takayama
    5. Hypergeometric and basic hypergeometric series and integrals associated with root systems Michael J. Schlosser
    6. Elliptic hypergeometric functions associated with root systems Hjalmar Rosengren and S. Ole Warnaar
    7. Dunkl operators and related special functions Charles F. Dunkl
    8. Jacobi polynomials and hypergeometric functions associated with root systems Gert J. Heckman and Eric M. Opdam
    9. Macdonald–Koornwinder polynomials Jasper V. Stokman
    10. Combinatorial aspects of Macdonald and related polynomials Jim Haglund
    11. Knizhnik–Zamolodchikov type equations, Selberg integrals, and related special functions Vitaly Tarasov and Alexander Varchenko
    12. 9j-Coefficients and higher Joris Van der Jeugt

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    Encyclopedia of Special Functions: The Askey-Bateman Project

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  • Editors

    Tom H. Koornwinder, Universiteit van Amsterdam
    Tom H. Koornwinder is Professor Emeritus at the University of Amsterdam. He is an expert in special functions, orthogonal polynomials, and Lie theory. He introduced the five-parameter extension of the BC-type Macdonald polynomials, which are nowadays called Koornwinder polynomials. He was co-author of the chapter on orthogonal polynomials in the Digital Library of Mathematical Functions, and is involved in its revision.

    Jasper V. Stokman, Universiteit van Amsterdam
    Jasper V. Stokman is Professor of Mathematics at the University of Amsterdam. He is an expert in special functions, Lie theory, and integrable systems. He introduced BC-type extensions of several families of classical orthogonal polynomials, and nonpolynomial generalizations of Koornwinder polynomials. He linked multivariable special functions to harmonic analysis on quantum groups and Hecke algebras, and to statistical mechanics and analytic number theory.


    Tom H. Koornwinder, Jasper V. Stokman, Yuan Xu, Keiji Matsumoto, Nobuki Takayama, Michael J. Schlosser, Hjalmar Rosengren, S. Ole Warnaar, Charles F. Dunkl, Gert J. Heckman, Eric M. Opdam, Jim Haglund, Vitaly Tarasov, Alexander Varchenko, Joris Van der Jeugt

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