Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions (eBook, PDF)

Redaktion: Koornwinder, Tom H.

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 15. Oktober 2020
• Englisch
• ISBN-13: 9781108916554
• Artikelnr.: 66183387

Inhaltsangabe

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; Index.