In the present paper, starting from the second-order difference hypergeomet
ric equation on the non-uniform lattice x(s) satisfied by the set of discre
te hypergeometric orthogonal q-polynomials {p(n)}, we find analytical expre
ssions of the expansion coefficients of any q-polynomials r(m)(x(s)) on x(s
) and of the product r(m)(x(s))q(j)(x(s)) in series of the set {p(n)}. Thes
e coefficients are given in terms of the polynomial coefficients of the sec
ond-order difference equations satisfied by the involved discrete hypergeom
etric q-polynomials, (C) 2001 Academic Press.