Weak classical orthogonal polynomials in two variables
type: Item
instance of: scholarly article
title: Weak classical orthogonal polynomials in two variables
zbMATH Open document ID: 1068.33019
author: Lidia Fernández
author: Teresa E. Pérez
author: Miguel A. Piñar
published in: Journal of Computational and Applied Mathematics
publication date: 2005-04-18T00:00:00Z
review text: The paper contains 6 definitions, 3 lemmas, 4 propositions and 2 corollaries. The authors first introduce the concept of weak classical orthogonal polynomials in two variables. Next, three characterizations for weak classical orthogonal polynomials are established: the orthogonality of the gradients; the structure relation; and the matrix Bochner-type second-order partial differential equation. Then, some consequences of the characterizations are given. At the end, as a special case, the Krall and Sheffer classical orthogonal polynomials in two variables are recorded.
reviewed by: P. K. Mital
Mathematics Subject Classification ID: 33C50
Mathematics Subject Classification ID: 33C90
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 33C47
zbMATH DE Number: 2157668
zbMATH Keywords: weak classical orthogonal polynomials
zbMATH Keywords: Pearson differential equation
zbMATH Keywords: moment functional
MaRDI profile type: Publication
full work available at URL: j.cam.2004.08.010
OpenAlex ID: W2039353936
cites work: Orthogonal polynomials of several variables
cites work: Q4040931
cites work: Orthogonal polynomials in two variables and second-order partial differential equations
cites work: Partial differential equations having orthogonal polynomial solutions
cites work: Rodrigues type formula for multi-variate orthogonal polynomials
cites work: Q3378651
cites work: Q4090656
cites work: The Recursion Formulas for Orthogonal Polynomials innVariables
cites work: Orthogonality and Recursion Formulas for Polynomials in n Variables
cites work: Orthogonal polynomials in two variables
cites work: Orthogonal polynomial eigenfunctions of second-order partial differential equations
cites work: Bivariate version of the Hahn-Sonine theorem
cites work: Q3799100
cites work: Classical orthogonal polynomials: A functional approach
cites work: Classical orthogonal polynomials in the theory of Schrödinger equation
cites work: On Multivariate Orthogonal Polynomials
DOI: 10.1016/J.CAM.2004.08.010
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description: scientific article; zbMATH DE number 2157668