Exceptional Gegenbauer polynomials via isospectral deformation
Classical Analysis and ODEs
2021-10-11 v1
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.
Cite
@article{arxiv.2110.04059,
title = {Exceptional Gegenbauer polynomials via isospectral deformation},
author = {María~Ángeles García-Ferrero and David Gómez-Ullate and Robert Milson and James Munday},
journal= {arXiv preprint arXiv:2110.04059},
year = {2021}
}