Two variable Freud orthogonal polynomials and matrix Painlevé-type difference equations Bracciali, Cleonice F. Pérez Fernández, Teresa Encarnación Bivariate orthogonal polynomials Freud orthogonal polynomials Three term relations Matrix Painlevé-type difference equations We study bivariate orthogonal polynomials associated with Freud weight functions depending on real parameters. We analyse relations between the matrix coefficients of the three term relations for the orthonormal polynomials as well as the coefficients of the structure relations satisfied by these bivariate semiclassical orthogonal polynomials, also a matrix differentialdifference equation for the bivariate orthogonal polynomials is deduced. The extension of the Painlev´e equation for the coefficients of the three term relations to the bivariate case and a two dimensional version of the Langmuir lattice are obtained. 2022-09-30T08:59:51Z 2022-09-30T08:59:51Z 2022-08-22 journal article Published version: Cleonice F. Bracciali, Glalco S. Costa & Teresa E. Pérez (2022) Two variable Freud orthogonal polynomials and matrix Painlevé-type difference equations, Journal of Difference Equations and Applications, DOI: [10.1080/10236198.2022.2119140] https://hdl.handle.net/10481/77095 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Taylor & Francis