%0 Journal Article
%T Differential equations for discrete Jacobi-Sobolev orthogonal polynomials
%A Antonio J. Dur¨¢n
%A Manuel D. de la Iglesia
%J Mathematics
%D 2015
%I arXiv
%X The aim of this paper is to study differential properties of orthogonal polynomials with respect to a discrete Jacobi-Sobolev bilinear form with mass point at $-1$ and/or $+1$. In particular, we construct the orthogonal polynomials using certain Casorati determinants. Using this construction, we prove that when the Jacobi parameters $\alpha$ and $\beta$ are nonnegative integers the Jacobi-Sobolev orthogonal polynomials are eigenfunctions of a differential operator of finite order (which will be explicitly constructed). Moreover, the order of this differential operator is explicitly computed in terms of the matrices which define the discrete Jacobi-Sobolev bilinear form.
%U http://arxiv.org/abs/1510.02570v1