Bivariate Symmetric Discrete Orthogonal Polynomials

In this paper, we analyze second-order linear partial difference equations having bivariate symmetric orthogonal polynomial solutions. We present conditions to have admissible, potentially self-adjoint partial difference equations of hypergeometric type having orthogonal polynomial solutions. For these solutions, we give explicitly the matrix coefficients of the three-term recurrence relations they satisfy. Finally, conditions in order to have symmetric orthogonal polynomial solutions are presented.