Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials

Autores
Cagliero, Leandro Roberto; Koornwinder, Tom H.
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
For a two-parameter family of lower triangular matrices with entries involving Jacobi polynomials an explicit inverse is given, with entries involving a sum of two Jacobi polynomials. The formula simplifies in the Gegenbauer case and then one choice of the parameter solves an open problem in a recent paper by Koelink, van Pruijssen & Román. The two-parameter family is closely related to two two-parameter groups of lower triangular matrices, of which we also give the explicit generators. Another family of pairs of mutually inverse lower triangular matrices with entries involving Jacobi polynomials, unrelated to the family just mentioned, was given by J. Koekoek & R. Koekoek (1999). We show that this last family is a limit case of a pair of connection relations between Askey–Wilson polynomials having one of their four parameters in common.
Fil: Cagliero, Leandro Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Koornwinder, Tom H.. University of Amsterdam; Países Bajos
Materia
Jacobi Polynomials
Gegenbauer Polynomials
Inverses of Explicit Lower Triangular Matrices
Biorthogonal Systems
Askey–Wilson Polynomials
Connection Coefficients
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/32128
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/32128
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomialsCagliero, Leandro RobertoKoornwinder, Tom H.Jacobi PolynomialsGegenbauer PolynomialsInverses of Explicit Lower Triangular MatricesBiorthogonal SystemsAskey–Wilson PolynomialsConnection Coefficientshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1For a two-parameter family of lower triangular matrices with entries involving Jacobi polynomials an explicit inverse is given, with entries involving a sum of two Jacobi polynomials. The formula simplifies in the Gegenbauer case and then one choice of the parameter solves an open problem in a recent paper by Koelink, van Pruijssen & Román. The two-parameter family is closely related to two two-parameter groups of lower triangular matrices, of which we also give the explicit generators. Another family of pairs of mutually inverse lower triangular matrices with entries involving Jacobi polynomials, unrelated to the family just mentioned, was given by J. Koekoek & R. Koekoek (1999). We show that this last family is a limit case of a pair of connection relations between Askey–Wilson polynomials having one of their four parameters in common.Fil: Cagliero, Leandro Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Koornwinder, Tom H.. University of Amsterdam; Países BajosAcademic Press Inc Elsevier Science2014-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/32128Koornwinder, Tom H.; Cagliero, Leandro Roberto; Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials; Academic Press Inc Elsevier Science; Journal Of Approximation Theory; 193; 4-2014; 20-380021-9045CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jat.2014.03.016info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0021904514000604info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:11:46Zoai:ri.conicet.gov.ar:11336/32128instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:11:46.453CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
title Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
spellingShingle Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
Cagliero, Leandro Roberto
Jacobi Polynomials
Gegenbauer Polynomials
Inverses of Explicit Lower Triangular Matrices
Biorthogonal Systems
Askey–Wilson Polynomials
Connection Coefficients
title_short Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
title_full Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
title_fullStr Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
title_full_unstemmed Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
title_sort Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
dc.creator.none.fl_str_mv Cagliero, Leandro Roberto
Koornwinder, Tom H.
author Cagliero, Leandro Roberto
author_facet Cagliero, Leandro Roberto
Koornwinder, Tom H.
author_role author
author2 Koornwinder, Tom H.
author2_role author
dc.subject.none.fl_str_mv Jacobi Polynomials
Gegenbauer Polynomials
Inverses of Explicit Lower Triangular Matrices
Biorthogonal Systems
Askey–Wilson Polynomials
Connection Coefficients
topic Jacobi Polynomials
Gegenbauer Polynomials
Inverses of Explicit Lower Triangular Matrices
Biorthogonal Systems
Askey–Wilson Polynomials
Connection Coefficients
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv For a two-parameter family of lower triangular matrices with entries involving Jacobi polynomials an explicit inverse is given, with entries involving a sum of two Jacobi polynomials. The formula simplifies in the Gegenbauer case and then one choice of the parameter solves an open problem in a recent paper by Koelink, van Pruijssen & Román. The two-parameter family is closely related to two two-parameter groups of lower triangular matrices, of which we also give the explicit generators. Another family of pairs of mutually inverse lower triangular matrices with entries involving Jacobi polynomials, unrelated to the family just mentioned, was given by J. Koekoek & R. Koekoek (1999). We show that this last family is a limit case of a pair of connection relations between Askey–Wilson polynomials having one of their four parameters in common.
Fil: Cagliero, Leandro Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Koornwinder, Tom H.. University of Amsterdam; Países Bajos
description For a two-parameter family of lower triangular matrices with entries involving Jacobi polynomials an explicit inverse is given, with entries involving a sum of two Jacobi polynomials. The formula simplifies in the Gegenbauer case and then one choice of the parameter solves an open problem in a recent paper by Koelink, van Pruijssen & Román. The two-parameter family is closely related to two two-parameter groups of lower triangular matrices, of which we also give the explicit generators. Another family of pairs of mutually inverse lower triangular matrices with entries involving Jacobi polynomials, unrelated to the family just mentioned, was given by J. Koekoek & R. Koekoek (1999). We show that this last family is a limit case of a pair of connection relations between Askey–Wilson polynomials having one of their four parameters in common.
publishDate 2014
dc.date.none.fl_str_mv 2014-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/32128
Koornwinder, Tom H.; Cagliero, Leandro Roberto; Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials; Academic Press Inc Elsevier Science; Journal Of Approximation Theory; 193; 4-2014; 20-38
0021-9045
CONICET Digital
CONICET
url http://hdl.handle.net/11336/32128
identifier_str_mv Koornwinder, Tom H.; Cagliero, Leandro Roberto; Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials; Academic Press Inc Elsevier Science; Journal Of Approximation Theory; 193; 4-2014; 20-38
0021-9045
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jat.2014.03.016
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0021904514000604
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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