Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions

Tom H. Koornwinder, Jasper V. Stokman

• Publisher: Cambridge University Press
• Year: 2020
• Print ISBN: 9781107003736
• eBook ISBN: 9781108916554
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

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.

Table of contents

• Cover
• Half-title
• Title page
• Copyright information
• Contents
• List of Contributors
• Preface
• 1 General Overview of Multivariable Special Functions
• 2 Orthogonal Polynomials of Several Variables
• 3 Appell and Lauricella Hypergeometric Functions
• 4 A-Hypergeometric Functions
• 5 Hypergeometric and Basic Hypergeometric Series and Integrals Associated with Root Systems
• 6 Elliptic Hypergeometric Functions Associated with Root Systems
• 7 Dunkl Operators and Related Special Functions
• 8 Jacobi Polynomials and Hypergeometric Functions Associated with Root Systems
• 9 Macdonald–Koornwinder Polynomials
• 10 Combinatorial Aspects of Macdonald and Related Polynomials
• 11 Knizhnik–Zamolodchikov-Type Equations, Selberg Integrals and Related Special Functions
• 12 9j-Coefficients and Higher
• Index