$q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions (Memoirs of the American Mathematical Society) - Softcover

American Mathematical Society

Softcover

ISBN 10: 082182774X ISBN 13: 9780821827741

Publisher: American Mathematical Society, 2002

Synopsis

In this work, 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 well-known classes of orthogonal polynomials. A number of basic properties of these polynomials follow from our approach. This leads naturally to the evaluation of the Askey-Wilson 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 two-term transformations of these functions. We also lay some infrastructure for more general investigations in the future.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2002
• Language: English
• ISBN 10: 082182774X
• ISBN 13: 9780821827741
• Binding: Paperback
• Number of pages: 56