Rebocho, M. N.2020-02-062020-02-062016M.N. Rebocho, On Laguerre-Hahn affine orthogonal polynomials on the unit circle from matrix Sylvester equations, Integral Transforms and Special Functions 27, no.2 (2016) 78-93.http://hdl.handle.net/10400.6/9059In this paper are derived recurrences for the reflection coefficients of Laguerre–Hahn affine orthogonal polynomials on the unit circle, including a form of the discrete Painlevé equations dPV . The technique is based on the knowledge of the first-order differential equation for the Carathéodory function, combined with a reinterpretation, in the formalism of matrix Sylvester equations, of compatibility conditions for the differential systems satisfied by the polynomials.engHermitian linear functionalsOPUCLaguerre–Hahn affine classSylvester equationsdiscrete Painlevé equationsjournal article10.1080/10652469.2015.1092969