Laguerre-Freud equations for the recurrence coefficients of Dω semi-classical orthogonal polynomials of class one

The Laguerre-Freud equations giving the recurrence coefficients βn, γn of orthogonal polynomials with respect to a Dω semi-classical linear form are derived. Dω is the difference operator. The limit when ω → 0 are also investigated recovering known results. Applications to generalized Meixner polynomials of class one are also treated.