A semiclassical perspective on multivariate orthogonal polynomials
M. Alvarez de Morales, L. Fernández, T. E. Pérez, M. A. Piñar
Abstract
Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these polynomials including the analogous of the semiclassical Pearson differential equation, the structure relation and a differential--difference equation.
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