Second structure relation for semiclassical orthogonal polynomials

18 pages, no figures.-- MSC2000 codes: 42C05; 33C45.MR#: MR2289233 (2009a:33013)Zbl#: Zbl 1125.33008Classical orthogonal polynomials are characterized from their orthogonality and by a first or second structure relation. For the semiclassical orthogonal polynomials (a generalization of the classical ones), we find only the first structure relation in the literature. In this paper, we establish a second structure relation. In particular, we deduce it by means of a general finite-type relation between a semiclassical polynomial sequence and the sequence of its monic derivatives.The work of the first author (F. M.) was supported by Dirección General de Investigación (Ministerio de Educación y Ciencia) of Spain under Grant BFM 2003-06335-C03-02 and INTAS Research Network NeCCA INTAS 03-51-6637. The second author (R. S.) was supported by Entreprise Kilani Gabès and Faculté des Sciences de Gabès, Tunisie.Publicad