Atia, Mohamed JalelMarcellán Español, Francisco JoséÁlvarez Rocha, Ignacio2009-12-102009-12-102002Facta Universitatis Series Mathematics and Informatics, 2002, vol. 17, p. 13-340352-9665http://hdl.handle.net/10016/600122 pages, no figures.-- MSC2000 codes: Primary 33C45, 33C47.MR#: MR2016752 (2005h:33018)Zbl#: Zbl 1081.33009In this paper the integral representation of any solution of the distributional equation S$ D((x -x)u)+((\mu-2\alpha-s-3)x -sx-\mu+1)u=0 $$ is obtained in an alternative and more natural way than the one derived from the method given in [4]. A particular quasi-definite case is studied and some properties for the corresponding sequence of orthogonal polynomials are obtained. Explicit expressions for the moments and for the recurrence coefficients are given using the Laguerre-Freud equations as the basic tool.application/pdfeng© University of NišDistributional equationSemiclassical orthogonal polynomialsQuasi-definite functionalresearch articleMatemáticasopen access