Fourth-order difference equation satisfied by the co-recursive of q-classical orthogonal polynomials

We derive the fourth-order q-difference equation satisfied by the co-recursive of q-classical orthogonal polynomials. The coefficients of this equation are given in terms of the polynomials phi and psi appearing in the q-Pearson difference equation D-q(phi rho) = psi rho defining the weight rho of the q-classical orthogonal polynomials inside the q-Hahn tableau. Use of suitable change of variable and limit processes allow us to recover the results known for the co-recursive of the classical continuous and classical discrete orthogonal polynomials. Moreover, we describe particular situations for which the co-recursive of classical orthogonal polynomials are still classical and express these new families in terms of the starting ones. (C) 2001 Elsevier Science B.V. All rights reserved.