Askey-Wilson functions of the first and second kind: Series and integral representations of \(C^ 2_ n(x ;\beta{}|{}q)+D^ 2_ n(x ;\beta{}|{}q)\)
type: Item
instance of: scholarly article
title: Askey-Wilson functions of the first and second kind: Series and integral representations of \(C^ 2_ n(x ;\beta{}|{}q)+D^ 2_ n(x ;\beta{}|{}q)\)
zbMATH Open document ID: 0765.33012
DOI: 10.1016/0022-247X(92)90156-8
author: Mizan Rahman
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: The author finds series and integral representations for the Askey-Wilson functions of first and second kind, namely, \(C_ n^ 2(x;\beta\mid q)\) and \(D_ n^ 2(x;\beta\mid q)\). The functions are expressed in terms of a particular \(_ 5\Phi_ 4\). The integral representation makes use of a well known representation due to Askey. The expression (4.1) for the square of \(| S_ \lambda|\) seems to have some printing errors. It is also not mentioned that the parameter `\(a\)' in (4.1) is a real and not a complex number.
Mathematics Subject Classification ID: 33C60
Mathematics Subject Classification ID: 33C55
zbMATH DE Number: 60592
zbMATH Keywords: ultra spherical polynomials
zbMATH Keywords: Askey-Wilson functions
reviewed by: R. P. Agarwal
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 60592