@UNPUBLISHED{publication1, title = "A characterization theorem for semi-classical orthogonal polynomials on non uniform lattices", author = "{BRANQUINHO, Am{\ยด{i}}lcar} and {CHEN, Yang} and {FILIPUK, Galina} and {REBOCHO, Maria das Neves}", year = "2018-03-19", abstract = "It is proved a characterization theorem for semi-classical orthogonal polynomials on non-uniform lattices that states the equivalence between the Pearson equation for the weight and some systems involving the orthogonal polynomials as well as the functions of the second kind. As a consequence, it is deduced the analogue of the so-called compatibility conditions in the ladder operator scheme. The classical orthogonal polynomials on non-uniform lattices are then recovered under such compatibility conditions, through a closed formula for the recurrence coefficients. ", url = "http://www.mat.uc.pt/preprints/eng\_2018.html", note = "" }