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18 pages, no figures.-- MSC2000 codes: 42C05; 33C45. MR#: MR2289233 (2009a:33013) Zbl#: Zbl 1125.33008 Classical 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. Publicado

Usually, coherent pairs of orthogonal polynomials have been considered in the wider context of Sobolev orthogonality. In this paper, we focus our attention on the problem of coherence between two orthogonal polynomial sequences in terms of the corresponding linear functionals. We deduce some conditions about the linear functionals in order that the corresponding orthogonal polynomial sequences constitute a coherent pair.