Second order partial differential equations for gradients of orthogonal polynomials in two variables

Authors:
Lidia Fernández;Teresa E. Pérez;Miguel A. Piñar
Affiliations:
Departamento de Matemática Aplicada, Universidad de Granada, Granada, Spain;Departamento de Matemática Aplicada and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada, Spain;Departamento de Matemática Aplicada and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada, Spain
Venue:
Journal of Computational and Applied Mathematics - Special issue: Special functions in harmonic analysis and applications
Year:
2007

Citing 5
Cited 1

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Abstract

In this work, we introduce the classical orthogonal polynomials in two variables as the solutions of a matrix second order partial differential equation involving matrix polynomial coefficients, the usual gradient operator, and the divergence operator. Here we show that the successive gradients of these polynomials also satisfy a matrix second order partial differential equation closely related to the first one.