eBook ISBN: | 978-1-4704-0350-8 |
Product Code: | MEMO/159/757.E |
List Price: | $51.00 |
MAA Member Price: | $45.90 |
AMS Member Price: | $30.60 |
eBook ISBN: | 978-1-4704-0350-8 |
Product Code: | MEMO/159/757.E |
List Price: | $51.00 |
MAA Member Price: | $45.90 |
AMS Member Price: | $30.60 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 159; 2002; 56 ppMSC: Primary 33; 05
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.
ReadershipGraduate students and research mathematicians interested in special functions and combinatorics.
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Table of Contents
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Chapters
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1. Introduction and preliminaries
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2. New results and connections with current research
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3. Vector operator identities and simple applications
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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.
-
Chapters
-
1. Introduction and preliminaries
-
2. New results and connections with current research
-
3. Vector operator identities and simple applications