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

Abstract

In the present paper, starting from the second-order difference hypergeometric equation on the non-uniform lattice x(s) satisfied by the set of discrete hypergeometric orthogonal q-polynomials {pn}, we find analytical expressions of the expansion coefficients of any q-polynomial rm(x(s)) on x(s) and of the product rm(x(s))qj(x(s)) in series of the set {pn}. These coefficients are given in terms of the polynomial coefficients of the second-order difference equations satisfied by the involved discrete hypergeometric q-polynomials.