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

13Citations
Citations of this article
4Readers
Mendeley users who have this article in their library.
Get full text

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.

Cite

CITATION STYLE

APA

Area, I., Godoy, E., Ronveaux, A., & Zarzo, A. (2012). Bivariate second-order linear partial differential equations and orthogonal polynomial solutions. Journal of Mathematical Analysis and Applications, 387(2), 1188–1208. https://doi.org/10.1016/j.jmaa.2011.10.024

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free