On a class of bivariate second-order linear partial difference equations and their monic orthogonal polynomial solutions |
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Authors: | I Area E Godoy J Rodal |
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Institution: | Departamento de Matemática Aplicada II, E.E. Telecomunicación, Universidade de Vigo, 36310-Vigo, Spain |
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Abstract: | In this paper we classify the bivariate second-order linear partial difference equations, which are admissible, potentially self-adjoint, and of hypergeometric type. Using vector matrix notation, explicit expressions for the coefficients of the three-term recurrence relations satisfied by monic orthogonal polynomial solutions are obtained in terms of the coefficients of the partial difference equation. Finally, we make a compilation of the examples existing in the literature belonging to the class analyzed in this paper, namely bivariate Charlier, Meixner, Kravchuk and Hahn orthogonal polynomials. |
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