Bivariate orthogonal polynomials in the Lyskova class

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Abstract

Classical orthogonal polynomials in two variables can be characterized as the polynomial solutions of a matrix second-order partial differential equation involving matrix polynomial coefficients. In this work, we study classical orthogonal polynomials in two variables whose partial derivatives satisfy again a second-order partial differential equation of the same type.

MSC

42C05
33C50

Keywords

Classical orthogonal polynomials in two variables
Lyskova class

Cited by (0)

Partially supported by Ministerio de Ciencia y Tecnología (MCYT) of Spain and by the European Regional Development Fund (ERDF) through the grant MTM 2005–08648–C02–02, and Junta de Andalucía, Grupo de Investigación FQM 0229.