Rebocho, M. N.Filipuk, Galina2020-02-042020-02-042018G. Filipuk and M.N. Rebocho, Differential equations for families of semi- classical orthogonal polynomials within class one, Applied Numerical Mathematics 124 (2018) 76-88.http://hdl.handle.net/10400.6/8998In this paper we study families of semi-classical orthogonal polynomials within class one. We derive general second or third order ordinary differential equations (with respect to certain parameters) for the recurrence coefficients of the three-term recurrence relation of these polynomials and show that in particular well-known cases, e.g. related to the modified Airy and Laguerre weights, these equations can be reduced to the second and the fourth Painlevé equations.engPainlev e equationsSemi-classical orthogonal polynomialsStieltjes functionpreprint