Connection problems for polynomial solutions of nonhomogeneous differential and difference equations
type: Item
instance of: scholarly article
title: Connection problems for polynomial solutions of nonhomogeneous differential and difference equations
zbMATH Open document ID: 0933.65147
DOI: 10.1016/S0377-0427(98)00155-1
author: A. Zarzo
author: Eduardo Godoy
author: A. Ronveaux
author: Iván Area
published in: Journal of Computational and Applied Mathematics
publication date: 1999-08-22T00:00:00Z
review text: The authors consider differential operators of the type \[ L[z(x)]= (s(x)D^2+ t(x)D+\lambda I)[z(x)], \] where \(s\) and \(t\) are polynomials, \(\lambda\) is a constant, \(D= d/dx\), as well as the corresponding discretized versions of such operators. They investigate the behavior of the solutions of differential resp. difference equations \[ L[z(x)]= Q_n(x), \] where \(Q_n\) is a polynomial. Expansions of the solutions with respect to the set of polynomials \(\{Q_n\}\) and a recurrence relation for the coefficients of this expansion are given. Some examples as well as extensions are also provided.
reviewed by: Guido Walz
Mathematics Subject Classification ID: 65Q05
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 1326366
zbMATH Keywords: polynomial solutions
zbMATH Keywords: nonhomogeneous differential equation
zbMATH Keywords: nonhomogeneous difference equation
zbMATH Keywords: recurrence relation
describes a project that uses: Mathematica
MaRDI profile type: Publication
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full work available at URL: s0377-0427(98)00155-1
OpenAlex ID: W2048892491
description: scientific article; zbMATH DE number 1326366