Multivariable Askey–Wilson function and bispectrality

For every positive integer d , we define a meromorphic function F d ( n ; z ), where n , z ∈ℂ d , which is a natural extension of the multivariable Askey–Wilson polynomials of Gasper and Rahman (Theory and Applications of Special Functions, Dev. Math., vol. 13, pp. 209–219, Springer, New York, 2005...

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Bibliographic Details
Published in:The Ramanujan journal Vol. 24; no. 3; pp. 273 - 287
Main Authors: Geronimo, Jeffrey S., Iliev, Plamen
Format: Journal Article
Language:English
Published: Boston Springer US 01.04.2011
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Bispectrality
33D50
Basic hypergeometric series
Multivariable orthogonal polynomials
39A70
ISSN:1382-4090, 1572-9303
Online Access:Get full text
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Summary:For every positive integer d , we define a meromorphic function F d ( n ; z ), where n , z ∈ℂ d , which is a natural extension of the multivariable Askey–Wilson polynomials of Gasper and Rahman (Theory and Applications of Special Functions, Dev. Math., vol. 13, pp. 209–219, Springer, New York, 2005 ). It is defined as a product of very-well-poised 8 φ 7 series and we show that it is a common eigenfunction of two commutative algebras and of difference operators acting on z and n , with eigenvalues depending on n and z , respectively. In particular, this leads to certain identities connecting products of very-well-poised 8 φ 7 series.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-010-9244-3