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q-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions (Memoirs of the American Mathematical Society)
Douglas Bowman
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Description for q-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions (Memoirs of the American Mathematical Society)
Paperback. Explores 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. This work also presents expansions of certain generalized basic hypergeometric functions in terms of the symmetric polynomials. Series: Memoirs of the American Mathematical Society. Num Pages: 56 pages, bibliography. BIC Classification: PBK; PBV. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 178 x 198 x 3. Weight in Grams: 146.
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 ... Read more
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 ... Read more
Product Details
Format
Paperback
Publication date
2002
Publisher
Amer Mathematical Society
Condition
New
Series
Memoirs of the American Mathematical Society
Place of Publication
Providence, United States
ISBN
9780821827741
SKU
V9780821827741
Shipping Time
Usually ships in 5 to 9 working days
Ref
99-3
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