Fourth-order differential equation for the co-modified of semi-classical orthogonal polynomials

摘要

We give a new derivation of the fourth-order differential equation satisfied by the co-modified (orthogonal polynomials) of any semi-classical family of orthogonal polynomials.This procedure generalizes a technique already used in the co-recursive and co-dilated cases. For the classical cases we give explicitly the corresponding differential equation in a determinantal form.