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

  • Area I
  • Godoy E
  • Ronveaux A
 et al. 
  • 4

    Readers

    Mendeley users who have this article in their library.
  • 11

    Citations

    Citations of this article.

Abstract

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. © 2011 Elsevier Inc.

Author-supplied keywords

  • 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

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free