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arXiv · 2110.04059

Exceptional Gegenbauer polynomials via isospectral deformation

María~Ángeles García-Ferrero·David Gómez-Ullate·Robert Milson·James Munday
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Abstract

We show a method to construct isospectral deformations of classical orthogonal polynomials. The construction is based on confluent Darboux transformations, and it allows to construct Sturm-Liouville problems with polynomial eigenfunctions that have an arbitrary number of continuous parameters. We propose to call these new orthogonal polynomial systems \emph{exceptional polynomials of the second kind}. We illustrate this construction by describing the class of exceptional Gegenbauer polynomials of the second kind.

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María~Ángeles García-Ferrero, David Gómez-Ullate, Robert Milson, James Munday. 2021-10-08. Exceptional Gegenbauer polynomials via isospectral deformation. https://arxiv.org/abs/2110.04059

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