Rebocho, M. N.Branquinho, A.2020-02-062020-02-062015A. Branquinho and M.N. Rebocho, Characterization theorem for Laguerre- Hahn orthogonal polynomials on non-uniform lattices, Journal of Mathematical Analysis and Applications 427, no. 1 (2015), 185-201.http://hdl.handle.net/10400.6/9058A characterization theorem for Laguerre–Hahn orthogonal polynomials on non-uniform lattices is stated and proved.This theorem proves the equivalence between the Riccati equation for the formal Stieltjes function, linear first-order difference relations for the orthogonal polynomials as well as for the associated polynomials of the first kind, and linear first-order difference relations for the functions of the second kind.engLaguerre-Hahn orthogonal polynomialsDivided difference operatorNon-uniform latticesRiccati difference equationStructure relationsjournal article