Expansions in series of orthogonal hypergeometric polynomials

Let us consider an arbitrary hypergeometric polynomial q(j)(x) and a set of orthogonal hypergeometric polynomials {p(n)(x)} in the domain of orthogonality Gamma. Here the expansion coefficients of x(m) and x(m)q(j)(x), m is an element of N-0, in series of the set {p(n)(x)} are found in terms of the polynomials sigma(x) and tau(x) characterizing the second-order differential equations satisfied by the involved hypergeometric polynomials. The resulting general expressions, which are given in an explicit and compact form, are used to produce known (for checking) and unknown expansions for various concrete classical orthogonal polynomials. (C) 1997 Elsevier Science B.V. All rights reserved.