Some semiclassical orthogonal polynomials of class one

Abstract

In this work, we will solve the Laguerre-Freud equations for the recurrence coefficients of the semiclassical orthogonal polynomials of class one in a particular case. The integral representation and, as a consequence, the moments of the corresponding form are obtained. Furthermore, both the characteristic elements of the structure relation and of the second-order differential equation are explicitly given.