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Orthogonal polynomials in two variables as solutions of higher order partial differential equations

Authors:	Lidia Fernández Teresa E Pérez Miguel A Piñar

Institution:	Departamento de Matemática Aplicada, and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada, Spain;Lenguajes y Systemas Informaticos e ingenieria de Software, Facultad de Informatica, Universidad Politecnica de Madrid, Campus de Montegancedo, Boadilla del Monte, Madrid, Spain 28660;Departamento de Matemáticas, Universidad Carlos III de Madrid Escuela Politécnica Superior, Av. Universidad 30 - 28911 LEGANES (Madrid), Spain;Departamento de Estad?´stica y Matemática Aplicada, Edificio CITE III, Desp. 256, Universidad de Almer?´a, 04120 Almer?´a, ESPAÑA (Spain)

Abstract:	Classical orthogonal polynomials in two variables can be characterized as the polynomial solutions of a second order partial differential equation involving polynomial coefficients. We study orthogonal polynomials in two variables which satisfy higher order partial differential equations. In particular, fourth order partial differential equations as well as some examples are studied.

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