Q-Difference Operators, Orthogonal Polynomials and Symmetric Expansions

Descripción:

Former library copy. Pages intact with possible writing/highlighting. Binding strong with minor wear. Dust jackets/supplements may not be included. Includes library markings. Stock photo provided. Product includes identifying sticker. Better World Books: Buy Books. Do Good. N° de ref. del artículo 5559268-6

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Sinopsis:

Reseña del editor: 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.