q-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions (Memoirs of the American Mathematical Society, Band 757) - Softcover

Bowman, Douglas

 
9780821827741: q-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions (Memoirs of the American Mathematical Society, Band 757)
Softcover
ISBN 10: 082182774X ISBN 13: 9780821827741
Verlag: American Mathematical Society, 2002

Inhaltsangabe

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.

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Verlag
American Mathematical Society
Erscheinungsdatum
2002
Sprache
Englisch
ISBN 10 
082182774X
ISBN 13 
9780821827741
Einband
Taschenbuch
Anzahl der Seiten
56
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