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Memoirs of the American Mathematical Society
2002; 56 pp; softcover
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 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.
Graduate students and research mathematicians interested in special functions and combinatorics.
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