Branquinho, A.Paiva, AnabelaRebocho, M. N.2020-02-042020-02-042013A. Branquinho, A. Paiva, and M.N. Rebocho, Sylvester equations for Laguerre-Hahn orthogonal polynomials on the real line, Applied Mathematics and Computation 219 (17) (2013), 9118-9131.http://hdl.handle.net/10400.6/9004Matrix Sylvester differential equations are introduced in the study of Laguerre-Hahn orthogonal polynomials. Matrix Sylvester differential systems are shown to yield representations for the Laguerre-Hahn orthogonal polynomials. Lax pairs are given, formed from the differential system and the recurrence relation, that yield discrete non-linear equations for the three term recurrence relation coefficients of the Laguerre-Hahn orthogonal polynomials.engOrthogonal polynomials on the real lineStieltjes functionRiccati differential equationMatrix Sylvester differential equationspreprint