aDepartamento de Matemáticas, Universidad Carlos III de Madrid, Spain
bDépartement des Méthodes Quantitatives, Institut Supérieur de Gestion de Gabès, Avenue Jilani Habib 6002, Gabès, Tunisie
Abstract:
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.