Matrix Pearson Equations Satisfied by Koornwinder Weights in Two Variables |
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| Authors: | Francisco Marcellán Misael Marriaga Teresa E. Pérez Miguel A. Piñar |
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| Affiliation: | 1.Instituto de Ciencias Matemáticas (ICMAT) and Departamento de Matemáticas,Universidad Carlos III de Madrid,Leganés,Spain;2.Departamento de Matemáticas,Universidad Carlos III de Madrid,Leganés,Spain;3.IEMath—Math. Institute and Departamento de Matemática Aplicada, Facultad de Ciencias,Universidad de Granada,Granada,Spain |
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| Abstract: | We consider Koornwinder’s method for constructing orthogonal polynomials in two variables from orthogonal polynomials in one variable. If semiclassical orthogonal polynomials in one variable are used, then Koornwinder’s construction generates semiclassical orthogonal polynomials in two variables. We consider two methods for deducing matrix Pearson equations for weight functions associated with these polynomials, and consequently, we deduce the second order linear partial differential operators for classical Koornwinder polynomials. |
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