Difference Equation for Modifications of Meixner Polynomials

We consider a modification of Meixner moment functional by adding a mass point at x = 0. We obtain the resulting orthogonal polynomials, identify them as hypergeometric 3F2 functions, and derive the second order difference equation which these polynomials satisfy. In such a way we give the solution to a problem raised by R. Askey (1991) in "Orthogonal Polynomials and Their Applications," p. 418, Baltzer AG Scientific, (Basel).