A generalization of a theorem of Bochner
type: Item
instance of: scholarly article
title: A generalization of a theorem of Bochner
zbMATH Open document ID: 1043.33009
DOI: 10.1016/S0377-0427(03)00536-3
author: Mourad E. H. Ismail
published in: Journal of Computational and Applied Mathematics
publication date: 2003-11-20T00:00:00Z
review text: A theorem of \textit{S.~Bochner} [Über Sturm-Liouvillesche Polynomsysteme, Math. Z. 29, 730--736 (1929; JFM 55.0260.01)] for classifying polynomial solutions to a certain second order differential equation is generalized to the \(q\)-hypergeometric case. To this end, the ordinary differential operators are replaced by the Askey-Wilson divided difference operators. The solutions, which have been Jacobi, Laguerre, and Bessel polynomials in Bochner's case, then turn out to be variants of Askey-Wilson polynomials.
reviewed by: Axel Riese
Mathematics Subject Classification ID: 33D45
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 39A70
zbMATH DE Number: 2006400
zbMATH Keywords: Bochner's theorem
zbMATH Keywords: orthogonal polynomials
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2006400