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In this paper, a fourth-order partial divided-difference equation onquadratic lattices with polynomial coefficients satisfied by bivariate Racahpolynomials is presented. From this equation we obtain explicitly the matrixcoefficients appearing in the three-term recurrence relations satisfied by anybivariate orthogonal polynomial solution of the equation. In particular, weprovide explicit expressions for the matrices in the three-term recurrencerelations satisfied by the bivariate Racah polynomials introduced by Tratnik.Moreover, we present the family of monic bivariate Racah polynomials definedfrom the three-term recurrence relations they satisfy, and we solve theconnection problem between two different families of bivariate Racahpolynomials. These results are then applied to other families of bivariateorthogonal polynomials, namely the bivariate Wilson, continuous dual Hahn andcontinuous Hahn, the latter two through limiting processes. The fourth-orderpartial divided-difference equations on quadratic lattices are shown to be ofhypergeometric type in the sense that the divided-difference derivatives ofsolutions are themselves solution of the same type of divided-differenceequations.

Linear partial divided-difference equation satisfied by multivariate orthogonal polynomials on quadratic lattices