Rebocho, M. N.2020-02-052020-02-052020Laguerre-Hahn orthogonal polynomials on the real line, Random Matrices: Theory and Applications, 8, no. 2 (2020) 2040001 (33 pages).http://hdl.handle.net/10400.6/9028A survey is given on sequences of orthogonal polynomials related to Stieltjes functions satisfying a Riccati type differential equation with polynomial coeffcients - the so-called Laguerre-Hahn class. The main goal is to describe analytical aspects, focusing on differential equations for those orthogonal polynomials, difference and differential equations for the recurrence coeffcients, and distributional equations for the corresponding linear functionals.engOrthogonal polynomialsStieltjes functionLaguerre-Hahn classDiscrete Painlev e equationsMatrix Sylvester equationspreprintDOI: 10.1142/S2010326320400018