Memoirs of the American Mathematical Society 2002; 56 pp; softcover Volume: 159 ISBN10: 082182774X ISBN13: 9780821827741 List Price: US$51 Individual Members: US$30.60 Institutional Members: US$40.80 Order Code: MEMO/159/757
 We explore ramifications and extensions of a \(q\)difference operator method first used by L.J. Rogers for deriving relationships between special functions involving certain fundamental \(q\)symmetric polynomials. In special cases these symmetric polynomials reduce to wellknown classes of orthogonal polynomials. A number of basic properties of these polynomials follow from our approach. This leads naturally to the evaluation of the AskeyWilson integral and generalizations. We also find expansions of certain generalized basic hypergeometric functions in terms of the symmetric polynomials. This provides us with a quick route to understanding the group structure generated by iterating the twoterm transformations of these functions. We also lay some infrastructure for more general investigations in the future. Readership Graduate students and research mathematicians interested in special functions and combinatorics. Table of Contents  Introduction and preliminaries
 New results and connections with current research
 Vector operator identities and simple applications
 Bibliography
