Differential equations for discrete Laguerre-Sobolev orthogonal polynomials

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. c ⃝ 2014 Elsevier Inc. All rights reserved.