Discrete Orthogonal Polynomials with Hypergeometric Weights and Painleve VI

We investigate the recurrence coefficients of discrete orthogonal polynomials on the non-negative integers with hypergeometric weights and show that they satisfy a system of non-linear difference equations and a non-linear second order differential equation in one of the parameters of the weights. The non-linear difference equations form a pair of discrete Painleve equations and the differential equation is the sigma-form of the sixth Painleve equation. We briefly investigate the asymptotic behavior of the recurrence coefficients as n -> infinity using the discrete Painleve equations.