The Fourth-order Difference Equation Satisfied by the Associated Orthogonal Polynomials of the Delta-Laguerre-Hahn Class

Starting from the D!-Riccati Diierence equation satissed by the Stieltjes function of a linear functional, we work out an algorithm which enables us to write the general fourth-order diierence equation satissed by the associated of any integer order of orthogonal polynomials of the-Laguerre-Hahn class. Moreover, in classical situations (Meixner, Charlier, Krawtchouk and Hahn), we give these diierence equations explicitly; and from the Hahn diierence equation, by limit processes we recover the diierence equations satissed by the associated of the classical discrete orthogonal polynomials and the diierential equations satissed by the associated of the classical continuous orthogonal polynomials.