Rebocho, M. N.Filipuk, Galina2020-02-042020-02-042017G. Filipuk and M.N. Rebocho, Orthogonal polynomials on systems of non-uniform lattices from compatibility conditions, Journal of Mathematical Analysis and Applications 456, no.2 (2017) 1380-1396.http://hdl.handle.net/10400.6/9000We deduce difference equations in the matrix form for Laguerre-Hahn orthogonal polynomials on systems of non-uniform lattices, the so-called compatibility conditions, involving the transfer matrices. As a consequence, we obtain closed form expressions for the recurrence relation coefficients of the Laguerre-Hahn polynomials of class zero.engOrthogonal polynomialsDivided-difference operatorNon-uniform latticesLaguerre-Hahn classpreprint