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Encyclopedia of Special Functions: The Askey-Bateman Project

Buch | Hardcover
434 Seiten
2020
Cambridge University Press (Verlag)
978-1-107-00373-6 (ISBN)
83,50 inkl. MwSt
The Encyclopedia of Special Functions provides an extensive update of the Bateman Manuscript Project. The three volumes will be indispensable for all scientists who use special functions in their research. Volume 2 provides detailed and up-to-date information on multivariable special functions.
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.

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 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.

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.

Erscheinungsdatum
Reihe/Serie Encyclopedia of Special Functions: The Askey-Bateman Project 3 Hardback Books ; Volume 2
Zusatzinfo Worked examples or Exercises; 6 Tables, black and white; 2 Halftones, black and white; 15 Line drawings, black and white
Verlagsort Cambridge
Sprache englisch
Maße 175 x 251 mm
Gewicht 890 g
Themenwelt Mathematik / Informatik Mathematik Analysis
ISBN-10 1-107-00373-3 / 1107003733
ISBN-13 978-1-107-00373-6 / 9781107003736
Zustand Neuware
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