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arXiv · 1309.6259

Differential equations for discrete Laguerre-Sobolev orthogonal polynomials

Antonio J. Durán·Manuel D. de la Iglesia
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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.

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Antonio J. Durán, Manuel D. de la Iglesia. 2013-09-24. Differential equations for discrete Laguerre-Sobolev orthogonal polynomials. https://arxiv.org/abs/1309.6259

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