  It is well known that the classical families of orthogonal polynomials are
characterized as eigenfunctions of a second order linear
differential/difference operator. In this paper we present a study of classical
orthogonal polynomials in a more general context by using the differential (or
difference) calculus and Operator Theory. In such a way we obtain a unified
representation of them. Furthermore, some well known results related to the
Rodrigues operator are deduced. A more general characterization Theorem that
the one given in [1] and [2] for the q-polynomials of the q-Askey and Hahn
Tableaux, respectively, is established. Finally, the families of Askey-Wilson
polynomials, q-Racah polynomials, Al-Salam & Carlitz I and II, and q-Meixner
are considered.
  [1] R. Alvarez-Nodarse. On characterization of classical polynomials. J.
Comput. Appl. Math., 196:320{337, 2006. [2] M. Alfaro and R. Alvarez-Nodarse. A
characterization of the classical orthogonal discrete and q-polynomials. J.
Comput. Appl. Math., 2006. In press.
