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arXiv · 2309.10059

On polynomial solutions of certain finite order ordinary differential equations

L. M. Anguas·D. Barrios Rolanía
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Abstract

Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well as the corresponding eigenvalues. Also, some linear transformations are applied to sequences of eigenfunctions and a necessary condition for this to be a sequence of eigenfunctions of a new differential operator is obtained. These results are applied to the particular case of classical Hermite polynomials.

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L. M. Anguas, D. Barrios Rolanía. 2023-09-18. On polynomial solutions of certain finite order ordinary differential equations. https://arxiv.org/abs/2309.10059

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