Second order partial differential equations for gradients of orthogonal polynomials in two variables |
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| Authors: | Lidia Fernández Teresa E Pérez Miguel A Piñar |
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| Institution: | 1. Departamento de Matemática Aplicada, Universidad de Granada,18071 Granada, Spain;2. Departamento de Matemática Aplicada and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain |
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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. |
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| Keywords: | Orthogonal polynomials in two variables Classical orthogonal polynomials Matrix Pearson equation |
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