Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Laguerre type
type: Item
instance of: scholarly article
title: Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Laguerre type
zbMATH Open document ID: 0965.42017
author: Henk Meijer
author: Teresa E. Pérez
author: Miguel A. Piñar
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-07-25T00:00:00Z
review text: All coherent pairs for Sobolev orthogonal polynomials were obtained in 1997 by \textit{H. G. Meijer} [J. Approximation Theory 89, No. 3, 321-343 (1997; Zbl 0880.42012)]. For Laguerre coherent pairs \((\psi_0,\psi_1)\) one of the measure has to be a Laguerre weight and the other is a modification of a Laguerre weight by a rational function and/or a Dirac measure. The asymptotics of the Sobolev orthogonal polynomials is worked out for both cases, using the well-known asymptotics of Laguerre polynomials (in particular Perron's formula in the complex plane).
reviewed by: Walter Van Assche
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1471629
zbMATH Keywords: Sobolev orthogonal polynomials
zbMATH Keywords: coherent pairs
zbMATH Keywords: Laguerre polynomials
zbMATH Keywords: Laguerre weight
zbMATH Keywords: asymptotics
MaRDI profile type: Publication
OpenAlex ID: W2035452734
cites work: Q5642828
cites work: On polynomials orthogonal with respect to certain Sobolev inner products
cites work: Orthogonal polynomials on Sobolev spaces: Old and new directions
cites work: An asymptotic result for Laguerre-Sobolev orthogonal polynomials
cites work: Laguerre-Sobolev orthogonal polynomials
cites work: Asymptotics of Sobolev orthogonal polynomials for coherent pairs of measures
cites work: Q4892493
cites work: Determination of all coherent pairs
cites work: Q4059363
DOI: 10.1006/JMAA.2000.6779
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description: scientific article; zbMATH DE number 1471629