Difference Equations for Generalized Meixner Polynomials

In this paper is introduced a system of polynomials orthogonal with respect to the classical discrete weight function for Meixner polynomials with an extra point mass added at x=0. A difference operator of infinite order is constructed for which these new polynomials are eigenfunctions and a second-order difference equation is given with polynomial coefficients, n-dependent and of at most degree 2, which these polynomials satisfy.