@misc{10498/27007,
year = {2022},
url = {http://hdl.handle.net/10498/27007},
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.},
organization = {Spanish MINECO through Juan de la Cierva fellowship FJC2019-039681-I, Spanish State Research Agency through BCAM Severo Ochoa excellence accreditation SEV-2017-0718, Basque Government through the BERC Programme 2022-2025, projects PGC2018-096504-B-C33 and RTI2018-100754-B-I00 from FEDER/Ministerio de Ciencia e Innovacion-Agencia Estatal de Investigacion, the European Union under the 2014-2020 ERDF Operational Programme, and the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia (project FEDER-UCA18-108393)},
publisher = {WILEY},
keywords = {confluent Darboux transformations},
keywords = {exceptional polynomials},
keywords = {Gegenbauer polynomials},
keywords = {isospectral deformations},
keywords = {Sturm–Liouville problems},
title = {Exceptional Gegenbauer polynomials via isospectral deformation},
doi = {10.1111/sapm.12510},
author = {García-Ferrero, María Ángeles and Gómez-Ullate Oteiza, David and Milson, Robert and Munday, James},
}