Exceptional Gegenbauer polynomials via isospectral deformation

Identificadores
URI: http://hdl.handle.net/10498/27007
DOI: 10.1111/sapm.12510
ISSN: 0022-2526
ISSN: 1467-9590
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2022Department
Ingeniería InformáticaSource
Stud Appl Math. 2022;1–40.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.
Subjects
confluent Darboux transformations; exceptional polynomials; Gegenbauer polynomials; isospectral deformations; Sturm–Liouville problemsCollections
- Artículos Científicos [5002]
- Articulos Científicos Ing. Inf. [142]