Abstract
The D-u-classical orthogonal polynomial sequences are defined through the D-u-Hahn's property: sequences that are orthogonal together with their D-u-first derivative, where D-u(p) = p' + u theta(0)p; for all p is an element of C[X]. We characterize them by means of a functional equation, a D-u-second order linear differential equation, the first and the second structure relations. A D-u-classical orthogonal sequence is especially a D-Laguerre-Hahn sequence of class less than or equal to two. A complete classification of the D-u-classical sequences is obtained. The functional equation coefficients, the structure relations coefficients, the three-term recurrence relation coefficients and the class are whenever given.