Differential equations for discrete Laguerre-Sobolev orthogonal polynomials
Classical Analysis and ODEs
2013-09-25 v1
Abstract
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.
Cite
@article{arxiv.1309.6259,
title = {Differential equations for discrete Laguerre-Sobolev orthogonal polynomials},
author = {Antonio J. Durán and Manuel D. de la Iglesia},
journal= {arXiv preprint arXiv:1309.6259},
year = {2013}
}