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Title: Exceptional Gegenbauer polynomials via isospectral deformation
Author: García-Ferrero, María Ángeles
Gómez-Ullate Oteiza, David
Milson, Robert
Munday, James
Keywords: Funcions hipergeomètriques
Teoria de l'aproximació
Hypergeometric functions
Approximation theory
Issue Date: 10-Jun-2022
Publisher: Wiley
Abstract: In this paper, we show how to construct exceptional orthogonal polynomials (XOP) using isospectral deformations of classical orthogonal polynomials. The construction is based on confluent Darboux transformations, where repeated factorizations at the same eigenvalue are allowed. These factorizations allow us to construct Sturm-Liouville problems with polynomial eigenfunctions that have an arbitrary number of realvalued parameters. We illustrate this new construction by exhibiting the class of deformed Gegenbauer polynomials, which are XOP families that are isospectral deformations of classical Gegenbauer polynomials.
Note: Reproducció del document publicat a:
It is part of: Studies in Applied Mathematics, 2022, vol. 149, num. 2, p. 324-363
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ISSN: 0022-2526
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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