Q-difference Operators, Orthogonal Polynomials and Symmetric Expansions: (Memoirs of the American Mathematical Society)
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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. bibliography
More Details
- Imprint: American Mathematical Society
- ISBN13: 9780821827741
- Packaged Weight: 170
- Format: Paperback
- Publisher: American Mathematical Society
- Release Date: 2002-08-30
- Series: Memoirs of the American Mathematical Society
- Binding: Paperback / softback
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