Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics

Detalhes bibliográficos
Autor(a) principal: Rebocho, M. N.
Data de Publicação: 2019
Outros Autores: Filipuk, Galina, Chen, Yang
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.6/8992
Resumo: In this paper we derive second and third order nonlinear difference equations for one of the recurrence coefficients in the three term recurrence relation of polynomials orthogonal with respect to a modified Laguerre weight. We show how these equations can be obtained from the Backlund transformations of the third Painlevé equation. We also show how to use nonlinear difference equations to derive a few terms in the formal asymptotic expansions in n of the recurrence coefficients.
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spelling Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptoticsOrthogonal polynomialsDifference equationsPainlev e equationsBacklund transformationsAsymptotic expansionsIn this paper we derive second and third order nonlinear difference equations for one of the recurrence coefficients in the three term recurrence relation of polynomials orthogonal with respect to a modified Laguerre weight. We show how these equations can be obtained from the Backlund transformations of the third Painlevé equation. We also show how to use nonlinear difference equations to derive a few terms in the formal asymptotic expansions in n of the recurrence coefficients..uBibliorumRebocho, M. N.Filipuk, GalinaChen, Yang2020-02-04T14:26:20Z20192019-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.6/8992engY. Chen, G. Filipuk, and M.N. Rebocho, Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics, Jaen Journal on Approximation 11, no. 1-2 (2019) 47-65.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-12-15T09:49:29Zoai:ubibliorum.ubi.pt:10400.6/8992Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:49:14.975563Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics
title Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics
spellingShingle Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics
Rebocho, M. N.
Orthogonal polynomials
Difference equations
Painlev e equations
Backlund transformations
Asymptotic expansions
title_short Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics
title_full Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics
title_fullStr Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics
title_full_unstemmed Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics
title_sort Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics
author Rebocho, M. N.
author_facet Rebocho, M. N.
Filipuk, Galina
Chen, Yang
author_role author
author2 Filipuk, Galina
Chen, Yang
author2_role author
author
dc.contributor.none.fl_str_mv uBibliorum
dc.contributor.author.fl_str_mv Rebocho, M. N.
Filipuk, Galina
Chen, Yang
dc.subject.por.fl_str_mv Orthogonal polynomials
Difference equations
Painlev e equations
Backlund transformations
Asymptotic expansions
topic Orthogonal polynomials
Difference equations
Painlev e equations
Backlund transformations
Asymptotic expansions
description In this paper we derive second and third order nonlinear difference equations for one of the recurrence coefficients in the three term recurrence relation of polynomials orthogonal with respect to a modified Laguerre weight. We show how these equations can be obtained from the Backlund transformations of the third Painlevé equation. We also show how to use nonlinear difference equations to derive a few terms in the formal asymptotic expansions in n of the recurrence coefficients.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01T00:00:00Z
2020-02-04T14:26:20Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.6/8992
url http://hdl.handle.net/10400.6/8992
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Y. Chen, G. Filipuk, and M.N. Rebocho, Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics, Jaen Journal on Approximation 11, no. 1-2 (2019) 47-65.
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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