\(q\)-difference operators for orthogonal polynomials
type: Item
instance of: scholarly article
title: \(q\)-difference operators for orthogonal polynomials
zbMATH Open document ID: 1185.39005
author: Mourad E. H. Ismail
author: Plamen Simeonov
published in: Journal of Computational and Applied Mathematics
publication date: 2009-11-04T00:00:00Z
review text: The families of orthogonal polynomials appearing as solutions of Sturm-Liouville differential equations support the operation of two adjoint linear differential operators which respectively raise and lower the degree. A similar theory has been developped for \(q\)-orthogonal polynomials and many results of the ``classical'' (differential) theory have been extended to the ``basic'' (\(q\)-analogue) theory, in particular by the authors of the paper reviewed here, which tackles indeterminate moment problems.
reviewed by: Jacques Sauloy
Mathematics Subject Classification ID: 39A13
Mathematics Subject Classification ID: 33D45
zbMATH DE Number: 5624886
zbMATH Keywords: \(q\)-difference equations
zbMATH Keywords: degree raising and lowering operators
zbMATH Keywords: Stieltjes-Wigert
zbMATH Keywords: \(q\)-Laguerre
zbMATH Keywords: Sturm-Liouville
zbMATH Keywords: \(q\)-orthogonal polynomials
zbMATH Keywords: indeterminate moment problems
MaRDI profile type: Publication
full work available at URL: j.cam.2009.02.044
OpenAlex ID: W2036044969
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DOI: 10.1016/J.CAM.2009.02.044
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description: scientific article; zbMATH DE number 5624886