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 relation coefficients.

%8 2018-10 %D 2018 %I ELSEVIER SCIENCE INC %J APPLIED MATHEMATICS AND COMPUTATION %P 356-366 %V 334 %@ 0096-3003 %U http://repository.umac.mo/handle/10692/106 %W UM