Q-difference Operators, Orthogonal Polynomials and Symmetric Expansions

American Mathematical Society (Autor)

Buch | Softcover

2002
American Mathematical Society (Verlag)
978-0-8218-2774-1 (ISBN)

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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.

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.

Introduction and preliminaries New results and connections with current research Vector operator identities and simple applications Bibliography.

Erscheint lt. Verlag	30.8.2002
Reihe/Serie	Memoirs of the American Mathematical Society
Zusatzinfo	bibliography
Verlagsort	Providence
Sprache	englisch
Gewicht	170 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	0-8218-2774-X / 082182774X
ISBN-13	978-0-8218-2774-1 / 9780821827741
Zustand	Neuware