$q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions (eBook)

Douglas Bowman (Autor)

eBook Download: PDF

56 Seiten
American Mathematical Society (Verlag)
978-1-4704-0350-8 (ISBN)

Infos

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.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Graphentheorie
• ISBN-10: 1-4704-0350-1 / 1470403501
• ISBN-13: 978-1-4704-0350-8 / 9781470403508