Rebocho, M. N.Filipuk, Galina2020-02-042020-02-042019G. Filipuk and M.N. Rebocho, Discrete semi-classical orthogonal polynomials of class one on quadratic lattices, Journal of Difference Equations and Applications 25, no. 1 (2019) 1-20.http://hdl.handle.net/10400.6/8993We study orthogonal polynomials on quadratic lattices with respect to a Stieltjes function, S, that satisfies a difference equation ADS = CMS+D; where A is a polynomial of degree less or equal than 3 and C is a polynomial of degree greater or equal than 1 and less or equal than 2. We show systems of difference equations for the orthogonal polynomials that arise from the so-called compatibility conditions. Some closed formulae for the recurrence relation coefficients are obtained.engDiscrete orthogonal polynomialsQuadratic latticeDivided-dierence operatorSemi-classical classjournal article