Pearson Equations for Discrete Orthogonal Polynomials: II. Generalized Charlier, Meixner and Hahn of type I cases

The Cholesky factorization of the moment matrix is considered for the generalized Charlier, generalized Meixner and generalized Hahn of type I discrete orthogonal polynomials. For the generalized Charlier we present an alternative derivation of the Laguerre-Freud relations found by Smet and Van Assche. Third order and second order order nonlinear ordinary differential equations are found for the recursion coefficient $gamma_n$. Laguerre-Freud relations are also found for the generalized Meixner case, which are compared with those of Smet and Van Assche. Finally, the generalized Hahn of type I discrete orthogonal polynomials are studied as well, and Laguerre-Freud equations are found and the differences with the equations found by Dominici and by Filipuk and Van Assche are given.