Bivariate orthogonal polynomials in the Lyskova class

Morales, María Álvarez de; Fernández, Lidia; Pérez, Teresa E.; Piñar, Miguel A.

doi:10.1016/j.cam.2009.02.027

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Vector Representation and Admissible Partial Differential Eq...1

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“…In order to present this study, we consider a bivariate class of linear partial differential equations, introduced as "the basic class" by Lyskova [22] for the multivariate case (see also [3]) and called here hypergeometric type equations:…”

Section: Vector Representation and Admissible Partial Differential Eq...mentioning

confidence: 99%

Bivariate second-order linear partial differential equations and orthogonal polynomial solutions

Area

Godoy

Ronveaux

et al. 2012

Journal of Mathematical Analysis and Applications

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In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second-order linear partial differential equations, which are admissible potentially self-adjoint and of hypergeometric type. General formulae for all these properties are obtained explicitly in terms of the polynomial coefficients of the partial differential equation, using vector matrix notation. Moreover, Rodrigues representations for the polynomial eigensolutions and for their partial derivatives of any order are given. Finally, as illustration, these results are applied to specific Appell and Koornwinder orthogonal polynomials, solutions of the same partial differential equation.

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Section: Vector Representation and Admissible Partial Differential Eq...mentioning

confidence: 99%