Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Jacobi type
type: Item
instance of: scholarly article
title: Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Jacobi type
zbMATH Open document ID: 0956.33004
DOI: 10.1016/S0377-0427(99)00102-8
author: Miguel A. Piñar
author: Henk Meijer
published in: Journal of Computational and Applied Mathematics
publication date: 2000-02-03T00:00:00Z
review text: The authors define a sequence of orthogonal polynomials with respect to the Sobolev inner product \[ (f,g)_S=\int f(x)g(x)d\psi_0(x)+\lambda\int f'(x)g'(x)d\psi_1(x) \] where \(\lambda\) and \(\{d\psi_0(x),d\psi_1(x)\}\) is a so-called coherent pair with at least one of the measures \(d\psi_0\) or \(\psi_1\) a Jacobi measure. The asymptotics of \(S_n(x)\) are investigated when \(n\to\infty\) and \(x\) fixed in a different interval.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1367891
zbMATH Keywords: Jacobi polynomial
zbMATH Keywords: Sobolev orthogonal polynomial
zbMATH Keywords: coherent pair
zbMATH Keywords: asymptotics
reviewed by: Matthew He
MaRDI profile type: Publication
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full work available at URL: s0377-0427(99)00102-8
OpenAlex ID: W2161693210
description: scientific article; zbMATH DE number 1367891