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 Title: Expansions in series of orthogonal hypergeometric polynomials Author(s): Sánchez-Ruiz, JorgeSánchez Dehesa, Jesús Publisher: Elsevier Issued date: 9-Mar-1998 Citation: Journal of Computational and Applied Mathematics, 1998, vol. 89, n. 1, p. 155-170 URI: http://hdl.handle.net/10016/6665 ISSN: 0377-0427 DOI: 10.1016/S0377-0427(97)00243-4 Description: 16 pages, no figures.-- MSC1991 codes: 33C45; 42C05.MR#: MR1625951 (99i:33012)Zbl#: Zbl 0944.33011 Abstract: 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 $x$ and $x q_j(x),\ m\in{\bf N}_0$, 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. Sponsor: 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. Review: PeerReviewed Publisher version: http://dx.doi.org/10.1016/S0377-0427(97)00243-4 Keywords: Orthogonal polynomialsHypergeometric differential equationExpansions of polynomials Rights: © Elsevier Appears in Collections: DM - GAMA - Artículos de Revistas