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.

'Overall the volume is a very useful addition to any research mathematician's library who works on these topics.' Manjil Pratim Saikia, zbMATH