First order non-homogeneous q-difference equation for Stieltjes function   characterizing q-orthogonal polynomials
  In this paper we give a characterization of some classical q-orthogonal polynomials in terms of a difference property of the associated Stieltjes function, i.e this function solves a first order non-homogeneous q-difference equation. The solutions of the aforementioned q-difference equation (given in terms of hypergeometric series) for some canonical cases, namely, q-Charlier, q-Kravchuk, q-Meixner and q-Hahn are worked out. 
J. Arves\'u and A. Soria-Lorente
math.CA math.ST stat.TH