Exceptional Jacobi polynomials which are deformations of Jacobi polynomials

In [10] we constructed new examples of exceptional Jacobi polynomials. The difference with the so called standard families is that the examples constructed in [10] depend on an arbitrary number of continuous parameters. Besides these continuous parameters, denoted by M = {Mo M1,...}, each one of the...

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Autor: Durán Guardeño, Antonio José
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/182367
Acceso en línea:https://hdl.handle.net/11441/182367
https://doi.org/10.1016/j.jmaa.2023.127523
Access Level:acceso abierto
Palabra clave:Orthogonal polynomials
Jacobi polynomials
Exceptional orthogonal polynomials
Exceptional Jacobi polynomials
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spelling Exceptional Jacobi polynomials which are deformations of Jacobi polynomialsDurán Guardeño, Antonio JoséOrthogonal polynomialsJacobi polynomialsExceptional orthogonal polynomialsExceptional Jacobi polynomialsIn [10] we constructed new examples of exceptional Jacobi polynomials. The difference with the so called standard families is that the examples constructed in [10] depend on an arbitrary number of continuous parameters. Besides these continuous parameters, denoted by M = {Mo M1,...}, each one of the new families of exceptional Jacobi polynomials is associated to two negative integers a < b < -1 and a finite set of positive integers F satisfying that {-b,...,-a -b -1} C F. In this paper we prove that when F = {u,u+1,..., -a -b -1}, with 1 < u < -b, the exceptional Jacobi polynomials are deformations of Jacobi polynomials (when the continuous parameters Mi -- 1. Otherwise, the exceptional Jacobi polynomials are deformations of standard exceptional Jacobi polynomials (again when the continuous parameters Mi --1).ElsevierAnálisis MatemáticoFQM262: Teoría de la Aproximación2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/182367https://doi.org/10.1016/j.jmaa.2023.127523reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Mathematical Analysis and Applications, 527 (1), 127523-1.10.1016/j.jmaa.2023.127523info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1823672026-06-17T12:51:07Z
dc.title.none.fl_str_mv Exceptional Jacobi polynomials which are deformations of Jacobi polynomials
title Exceptional Jacobi polynomials which are deformations of Jacobi polynomials
spellingShingle Exceptional Jacobi polynomials which are deformations of Jacobi polynomials
Durán Guardeño, Antonio José
Orthogonal polynomials
Jacobi polynomials
Exceptional orthogonal polynomials
Exceptional Jacobi polynomials
title_short Exceptional Jacobi polynomials which are deformations of Jacobi polynomials
title_full Exceptional Jacobi polynomials which are deformations of Jacobi polynomials
title_fullStr Exceptional Jacobi polynomials which are deformations of Jacobi polynomials
title_full_unstemmed Exceptional Jacobi polynomials which are deformations of Jacobi polynomials
title_sort Exceptional Jacobi polynomials which are deformations of Jacobi polynomials
dc.creator.none.fl_str_mv Durán Guardeño, Antonio José
author Durán Guardeño, Antonio José
author_facet Durán Guardeño, Antonio José
author_role author
dc.contributor.none.fl_str_mv Análisis Matemático
FQM262: Teoría de la Aproximación
dc.subject.none.fl_str_mv Orthogonal polynomials
Jacobi polynomials
Exceptional orthogonal polynomials
Exceptional Jacobi polynomials
topic Orthogonal polynomials
Jacobi polynomials
Exceptional orthogonal polynomials
Exceptional Jacobi polynomials
description In [10] we constructed new examples of exceptional Jacobi polynomials. The difference with the so called standard families is that the examples constructed in [10] depend on an arbitrary number of continuous parameters. Besides these continuous parameters, denoted by M = {Mo M1,...}, each one of the new families of exceptional Jacobi polynomials is associated to two negative integers a < b < -1 and a finite set of positive integers F satisfying that {-b,...,-a -b -1} C F. In this paper we prove that when F = {u,u+1,..., -a -b -1}, with 1 < u < -b, the exceptional Jacobi polynomials are deformations of Jacobi polynomials (when the continuous parameters Mi -- 1. Otherwise, the exceptional Jacobi polynomials are deformations of standard exceptional Jacobi polynomials (again when the continuous parameters Mi --1).
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/182367
https://doi.org/10.1016/j.jmaa.2023.127523
url https://hdl.handle.net/11441/182367
https://doi.org/10.1016/j.jmaa.2023.127523
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Mathematical Analysis and Applications, 527 (1), 127523-1.
10.1016/j.jmaa.2023.127523
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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