What is beyond coherent pairs of orthogonal polynomials?
type: Item
instance of: scholarly article
title: What is beyond coherent pairs of orthogonal polynomials?
zbMATH Open document ID: 0855.42016
DOI: 10.1016/0377-0427(95)00121-2
author: J. Petronilho
author: Miguel A. Piñar
author: Francisco Marcellán
author: Teresa E. Pérez
published in: Journal of Computational and Applied Mathematics
publication date: 1996-07-15T00:00:00Z
review text: Two quasi-definite linear functionals \(u_0\) and \(u_1\) constitute a coherent pair when the corresponding monic orthogonal polynomial systems, \(\{P_n\}_n\) and \(\{T_n\}_n\), satisfy \[ T_n (x) = {P_{n + 1}' (x) \over n + 1} - \sigma_n {P_n' (x) \over n},\;n \geq 1, \tag{*} \] where \(\sigma_n\) are nonzero real numbers. The authors fix one of the monic orthogonal polynomial systems \((P_n\) or \(T_n)\) and study conditions on \(\{\sigma_n\}\) that make the second sequence, given by (*), to be orthogonal. Furthermore, the symmetric coherence of \(u_0\) and \(u_1\) is defined by a relation analogous to (*), but where \(P_{n + 1}\) and \(P_{n - 1}\) are involved. The construction of symmetrically coherent pairs of functionals from the usual coherence is also investigated.
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 903579
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: symmetrically coherent pairs
reviewed by: Andrei Martínez Finkelshtein
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00121-2
OpenAlex ID: W2056596518
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description: scientific article; zbMATH DE number 903579