On the connection and linearization problem for discrete hypergeometric q-polynomials

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.