The fourth-order difference equation satisfied by the associated orthogonal polynomials of the D-q-Laguerre-Hahn class

We derive the general fourth-order difference equation satisfied by the ass ociated orthogonal polynomials of any integer order of the D-q-Laguerre-Hah n class. This difference equation is given explicitly for the q-classical o rthogonal polynomials, allowing us to recover by limit process the fourth-o rder differential equation satisfied by the associated classical continuous orthogonal polynomials. Finally, we give some applications on the first as sociated, the co-recursive and the co-recursive associated classical orthog onal polynomials.