q-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions - Couverture souple

American Mathematical Society

 
9780821827741: q-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions
Couverture souple
ISBN 10 : 082182774X ISBN 13 : 9780821827741
Editeur : American Mathematical Society, 2002

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2002
Langue
anglais
ISBN 10 
082182774X
ISBN 13 
9780821827741
Reliure
Broché
Nombre de pages
56
Coordonnées du fabricant
non disponible
Personne responsable
non disponible