The fourth-order difference equation satisfied by the associated orthogonal polynomials of the Delta-Laguerre-Hahn class

Starting from the D-w-Riccati difference equation satisfied by the Stieltje s function of a linear functional, we work out an algorithm which enables u s to write the general fourth-order difference equation satisfied by the as sociated of any integer order of orthogonal polynomials of the Delta-Laguer re-Hahn class. Moreover, in classical situations (Meixner, Charlier, Krawtc houk and Hahn), we give these difference equations explicitly; and from the Hahn difference equation, by limit processes we recover the difference equ ations satisfied by the associated of the classical discrete orthogonal pol ynomials and the differential equations satisfied by the associated of the classical continuous orthogonal polynomials. (C) 1999 Academic Press.