Recurrence coefficients and difference equations of classical discrete orthogonal and q-orthogonal polynomial sequences

We use the algebraic approach introduced in [15] for the study of orthogonal polynomial sequences to construct two families of polynomial sequences that extend the Hahn classes and include most of the classical discrete orthogonal and q-orthogonal polynomial sequences. For each family we obtain explicit formulas for the recurrence coefficients of all of its elements. We also characterize each family using difference and q-difference eigenvalue equations.