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Title of article :
On a class of bivariate second-order linear partial difference equations and their monic orthogonal polynomial solutions
Author/Authors :
Area، نويسنده , , I. and Godoy، نويسنده , , E. Padilla-Rodal، نويسنده , , J.، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2012
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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.
Keywords :
Second-order admissible potentially self-adjoint partial difference equations of hypergeometric type , Bivariate orthogonal polynomials of discrete variable , Generalized Kampé de Feriet hypergeometric series , Bivariate Charlier , Meixner , Kravchuk and Hahn polynomials
Journal title :
Journal of Mathematical Analysis and Applications
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