On the Connection and Linearization Problem for Discrete Hypergeometric q-Polynomials1

In the present paper, starting from the second-order difference hypergeometric equation on the non-uniform lattice xŽ s. satisfied by the set of discrete hypergeo- metric orthogonal q-polynomials pn4, we find analytical expressions of the expansion coefficients of any q-polynomial rmŽ xŽ s.. on xŽ s. and of the product rmŽ xŽ s..qjŽ xŽ s.. in series of the set pn4. These coefficients are given in terms of the polynomial coefficients of the second-order difference equations satisfied by the involved discrete hypergeometric q-polynomials.