Laguerre-Freud equations associated with the Hq-semiclassical forms of class one

Abstract

We give the system of Laguerre-Freud equations for the recurrence coefficients ?n, ?n+1, n ? 0 of orthogonal polynomials with respect to a Hq-semiclassical form (linear functional) of class one. The system is solved in the case when ?n = tn-1-tn and n+1 =-t2n with tn?0, n ? 0 and t-1 = 0. There are essentially three canonical cases.