Bivariate second-order linear partial differential equations and orthogonal polynomial solutions

In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second-order linear partial differential equations, which are admissible potentially self-adjoint and of hypergeometric type. General formulae for all th...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2012, Vol.387 (2), p.1188-1208
Main Authors: Area, I., Godoy, E., Ronveaux, A., Zarzo, A.
Format: Article
Language:English
Subjects:
Appell polynomials
Bivariate orthogonal polynomials
Connection problems
Generalized Kampé de Fériet hypergeometric series
Rodrigues formula
Second-order admissible potentially self-adjoint partial differential equations of hypergeometric type
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second-order linear partial differential equations, which are admissible potentially self-adjoint and of hypergeometric type. General formulae for all these properties are obtained explicitly in terms of the polynomial coefficients of the partial differential equation, using vector matrix notation. Moreover, Rodrigues representations for the polynomial eigensolutions and for their partial derivatives of any order are given. As illustration, these results are applied to a two parameter monic Appell polynomials. Finally, the non-monic case is briefly discussed.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.10.024