On Factorization and Solutions of q -difference Equations Satisfied by some Classes of Orthogonal Polynomials.

We derive and factorize the fourth-order q -difference equations satisfied by orthogonal polynomials obtained from some perturbations of the recurrence coefficients of q -classical orthogonal polynomials. These perturbations include the r th associated, the anti-associated, the general co-recursive, co-recursive associated, co-dilated and the general co-modified q -classical orthogonal polynomials. Moreover we find a basis of four linearly independent solutions of these fourth-order q -difference equations and express the modified families in terms of the starting ones. [ABSTRACT FROM AUTHOR]