Some generating functions for the associated Askey-Wilson polynomials
type: Item
instance of: scholarly article
title: Some generating functions for the associated Askey-Wilson polynomials
zbMATH Open document ID: 0861.33015
DOI: 10.1016/0377-0427(95)00249-9
author: Mizan Rahman
published in: Journal of Computational and Applied Mathematics
publication date: 1997-05-11T00:00:00Z
review text: The author obtains a new representation of the Askey-Wilson polynomial \(p^\alpha_n(x)\) as a finite double sum involving basic Pochhammer symbols. Moreover, a double integral representation over \([-1,1] \times [-1,1]\), and two generating functions for \(p^\alpha_n(x)\) are established. The results, which follow by lengthy series manipulations, are too long to reproduce here.
Mathematics Subject Classification ID: 33D45
Mathematics Subject Classification ID: 33D60
zbMATH DE Number: 908396
zbMATH Keywords: Askey-Wilson polynomial
reviewed by: Per W. Karlsson
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00249-9
OpenAlex ID: W1976563052
cites work: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
cites work: The Associated Ultraspherical Polynomials and their q-Analogues
cites work: Q4170993
cites work: Q4040884
cites work: Two Families of Associated Wilson Polynomials
cites work: The Associated Askey-Wilson Polynomials
cites work: Asymptotic and generating relations for the q-Jacobi and //\(4Phi_ 3\) polynomials
cites work: Explicit Formulas for the Associated Jacobi Polynomials and Some Applications
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description: scientific article; zbMATH DE number 908396