  The aim of this paper is to study differential properties of orthogonal
polynomials with respect to a discrete Laguerre-Sobolev bilinear form with mass
point at zero. In particular we construct the orthogonal polynomials using
certain Casorati determinants. Using this construction, we prove that they are
eigenfunctions of a differential operator (which will be explicitly
constructed). Moreover, the order of this differential operator is explicitly
computed in terms of the matrix which defines the discrete Laguerre-Sobolev
bilinear form.
