CRM Proceedings & Lecture Notes 1999; 276 pp; softcover Volume: 22 ISBN10: 0821820265 ISBN13: 9780821820261 List Price: US$96 Member Price: US$76.80 Order Code: CRMP/22
 There has been revived interest in recent years in the study of special functions. Many of the latest advances in the field were inspired by the works of R. A. Askey and colleagues on basic hypergeometric series and I. G. Macdonald on orthogonal polynomials related to root systems. Significant progress was made by the use of algebraic techniques involving quantum groups, Hecke algebras, and combinatorial methods. The CRM organized a workshop for key researchers in the field to present an overview of current trends. This volume consists of the contributions to that workshop. Topics include basic hypergeometric functions, algebraic and representationtheoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems. Titles in this series are copublished with the Centre de Recherches Mathématiques. Readership Graduate students and research mathematicians interested in special functions, combinatorics, representation theory, harmonic analysis, quantum groups, integrable systems, and mathematical physics; theoretical physicists. Table of Contents  F. Bergeron and A. M. Garsia  Science fiction and Macdonald's polynomials
 R. Chouikha  On the expansion of elliptic functions and applications
 D. V. Chudnovsky and G. V. Chudnovsky  Generalized hypergeometric functionsClassification of identities and explicit rational approximations
 W. S. Chung, E. G. Kalnins, and W. Miller, Jr.  Tensor products of \(q\)superalgebras and \(q\)series identities. I
 J. F. van Diejen and J. V. Stokman  \(q\)Racah polynomials for \(BC\) type root systems
 C. F. Dunkl  Intertwining operators of type \(B_N\)
 R. Floreanini, J. LeTourneux, and L. Vinet  Symmetries and continuous \(q\)orthogonal polynomials
 P. G. A. Floris  Addition theorems for spherical polynomials on a family of quantum spheres
 F. A. Grünbaum and L. Haine  On a \(q\)analogue of the string equation and a generalization of the classical orthogonal polynomials
 M. E. H. Ismail, D. R. Masson, and S. K. Suslov  The \(q\)Bessel function on a \(q\)quadratic grid
 D. Kim and D. Stanton  Three statistics on lattice paths
 A. N. Kirillov  Quantum Grothendieck polynomials
 A. N. Kirillov and M. Noumi  \(q\)difference raising operators for Macdonald polynomials and the integrality of transition coefficients
 B. A. Kupershmidt  Great powers of \(q\)calculus
 V. Spiridonov  \(q\)special functions: Differentialdifference equations, roots of unity, and all that
 A. Strasburger  On algebras of creation and annihilation operators
