Expansions in series of orthogonal hypergeometric polynomials

16 pages, no figures.-- MSC1991 codes: 33C45; 42C05.MR#: MR1625951 (99i:33012)Zbl#: Zbl 0944.33011Let 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 $x^mq_j(x),\ m\in{\bf N}_0$, 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 hypergeometric polynomials involved. 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.This work has been partially supported by the European project INTAS-93-219-ext. The first author also acknowledges the partial financial support of the Fundació Aula (Barcelona, Spain). The second author has been also partially supported by the Dirección General de Enseñanza Superior (DGES) of Spain under grant PB 95-1205 and by the Junta de Andalucía FQM207.Publicad