Branquinho, A.Rebocho, M. N.2020-02-062020-02-062011A. Branquinho and M.N. Rebocho, Difference and differential equations for deformed Laguerre-Hahn orthogonal polynomials on the unit circle, Journal of Physics A: Mathematical and Theoretical 44 (46) (2011), 465204.http://hdl.handle.net/10400.6/9057Sequences of orthogonal polynomials on the unit circle whose Carath´eodory function satisfies a Riccati-type differential equation with polynomial coefficients are studied. We deduce discrete Lax equations which lead to difference equations for the corresponding sequences of reflection parameters, and we analyze the continuous differential equations that arise when deformations through a dependence on a parameter t occur.engOrthogonal polynomialsjournal article