# Exceptional Gegenbauer polynomials via isospectral deformation

@inproceedings{GarciaFerrero2021ExceptionalGP, title={Exceptional Gegenbauer polynomials via isospectral deformation}, author={Mar'ia 'Angeles Garc'ia-Ferrero and David G'omez-Ullate and Robert Milson and James Munday}, year={2021} }

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 exceptional polynomials of the second kind. We illustrate this construction by describing the class of exceptional Gegenbauer polynomials of the…

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