Resumen de Differential equations for discrete Laguerre–Sobolev orthogonal polynomials
Antonio José Durán Guardeño, Manuel D. de la Iglesia
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.
