ENCYCLOPEDIA OF SPECIAL FUNCTIONS: THE ASKEY-BATEMAN PROJECT - ENCYCLOPEDIA VOLUME 2

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.