Expansions in series of orthogonal hypergeometric polynomials

Let us consider an arbitrary hypergeometric polynomial qj(x) and a set of orthogonal hypergeometric polynomials ∗pn(x)∗ in the domain of orthogonality Γ. Here the expansion coefficients of xm and xmqj(x), m∈N0, in series of the set ∗pn(x)∗ are found in terms of the polynomials σ(x) and τ(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.