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arXiv · 1510.02570

Differential equations for discrete Jacobi-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 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.

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Antonio J. Durán, Manuel D. de la Iglesia. 2015-10-09. Differential equations for discrete Jacobi-Sobolev orthogonal polynomials. https://arxiv.org/abs/1510.02570

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