An integral representation and some transformation properties of q-Bessel functions
type: Item
instance of: scholarly article
title: An integral representation and some transformation properties of q-Bessel functions
zbMATH Open document ID: 0634.33013
DOI: 10.1016/0022-247X(87)90164-8
author: Mizan Rahman
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: As long ago as 1903, \textit{F. H. Jackson} [Trans. Roy. Soc. Edin. 41, 1-28 (1903)] introduced two q-analogues of the Bessel function of the first kind. The main object of this paper is to deduce a q-integral of Poisson type for the basic Bessel functions. In the analysis, the main tool used is a q-analogue of the Euler integral representation of the function \({}_ 2F_ 1\). (see \textit{B. Nassrallah} and \textit{M. Rahman}, SIAM J. Math. Anal. 16, 186-197 (1985; Zbl 0564.33009)]. In the sequel, quadratic transformations and q-analogues of certain results by Gegenbauer are obtained.
reviewed by: H. Exton
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 4032100
zbMATH Keywords: basic Bessel functions
zbMATH Keywords: quadratic transformations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4032100