Structure relations for orthogonal polynomials
type: Item
instance of: scholarly article
title: Structure relations for orthogonal polynomials
zbMATH Open document ID: 1166.42014
author: Mourad E. H. Ismail
published in: Pacific Journal of Mathematics
publication date: 2009-04-08T00:00:00Z
review text: This paper is devoted to study how to derive structure relations for general orthogonal polynomials, that is, to find operators whose action on \(p_n\) is a combination of \(p_n\) and \(p_{n+1}\) with variable coefficients. The results of \textit{T. H. Koornwinder} [J. Comput. Appl. Math. 207, No. 2, 214--226 (2007; Zbl 1120.33018)] about structure relations with constant coefficients are generalized to differential operators and polynomials orthogonal with respect to some exponential weight functions. The aproach given here uses an alternative to the Sturm-Liouville property for the orthogonal polynomials. Moreover, the results of \textit{G. Bangerezako} [J. Comput. Appl. Math. 107, No. 2, 219--232 (1999; Zbl 0933.39042)] are also extended to a more general class of weight functions. Finally, the orthogonal polynomials with respect to a generalized Jacobi weight evolved under a Toda-type modification are also treated.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33C47
Mathematics Subject Classification ID: 33D45
zbMATH DE Number: 5541996
zbMATH Keywords: General orthogonal polynomials
zbMATH Keywords: Freud weights
zbMATH Keywords: Askey-Wilson type polynomials
zbMATH Keywords: Jacobi-Toda weights
MaRDI profile type: Publication
full work available at URL: pjm.2009.240.309
OpenAlex ID: W2059764026
DOI: 10.2140/PJM.2009.240.309
description: scientific article; zbMATH DE number 5541996