  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.
