Asymptotic properties of generalized Laguerre orthogonal polynomials

In the present paper we deal with the polynomials L(α,M,N) n (x) orthogonal with respect to the Sobolev inner product (p, q) = 1 Γ(α+1) Z ∞ 0 p(x)q(x) x α e −x dx + M p(0)q(0) + N p 0 (0)q 0 (0), N,M ≥ 0, α > −1, firstly introduced by Koekoek and Meijer in 1993 and extensively studied in the last...

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Autores: Álvarez Nodarse, Renato, Moreno Balcázar, Juan José
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2004
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41725
Acceso en línea:http://hdl.handle.net/11441/41725
https://doi.org/10.1016/S0019-3577(04)90012-2
Access Level:acceso abierto
Palabra clave:Asymptotics
Laguerre polynomials
generalized Laguerre polynomials
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spelling Asymptotic properties of generalized Laguerre orthogonal polynomialsÁlvarez Nodarse, RenatoMoreno Balcázar, Juan JoséAsymptoticsLaguerre polynomialsgeneralized Laguerre polynomialsIn the present paper we deal with the polynomials L(α,M,N) n (x) orthogonal with respect to the Sobolev inner product (p, q) = 1 Γ(α+1) Z ∞ 0 p(x)q(x) x α e −x dx + M p(0)q(0) + N p 0 (0)q 0 (0), N,M ≥ 0, α > −1, firstly introduced by Koekoek and Meijer in 1993 and extensively studied in the last years. We present some new asymptotic properties of these polynomials and also a limit relation between the zeros of these polynomials and the zeros of Bessel function Jα(x). The results are illustrated with numerical examples. Also, some general asymptotic formulas for generalizations of these polynomials are conjectured.Junta de AndalucíaDirección General de InvestigaciónUnión EuropeaElsevierAnálisis Matemático2004info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/41725https://doi.org/10.1016/S0019-3577(04)90012-2reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésIndagationes Mathematicae, 15 (2), 151-165.FQM 0262BFM 2000-0206-C04-02info:eu-repo/grantAgreement/EC/INTAS-2000-00272/FQM 0229BFM 2001-3878-C02-02http://dx.doi.org/10.1016/S0019-3577(04)90012-2info:eu-repo/semantics/openAccessoai:idus.us.es:11441/417252026-06-17T12:51:07Z
dc.title.none.fl_str_mv Asymptotic properties of generalized Laguerre orthogonal polynomials
title Asymptotic properties of generalized Laguerre orthogonal polynomials
spellingShingle Asymptotic properties of generalized Laguerre orthogonal polynomials
Álvarez Nodarse, Renato
Asymptotics
Laguerre polynomials
generalized Laguerre polynomials
title_short Asymptotic properties of generalized Laguerre orthogonal polynomials
title_full Asymptotic properties of generalized Laguerre orthogonal polynomials
title_fullStr Asymptotic properties of generalized Laguerre orthogonal polynomials
title_full_unstemmed Asymptotic properties of generalized Laguerre orthogonal polynomials
title_sort Asymptotic properties of generalized Laguerre orthogonal polynomials
dc.creator.none.fl_str_mv Álvarez Nodarse, Renato
Moreno Balcázar, Juan José
author Álvarez Nodarse, Renato
author_facet Álvarez Nodarse, Renato
Moreno Balcázar, Juan José
author_role author
author2 Moreno Balcázar, Juan José
author2_role author
dc.contributor.none.fl_str_mv Análisis Matemático
dc.subject.none.fl_str_mv Asymptotics
Laguerre polynomials
generalized Laguerre polynomials
topic Asymptotics
Laguerre polynomials
generalized Laguerre polynomials
description In the present paper we deal with the polynomials L(α,M,N) n (x) orthogonal with respect to the Sobolev inner product (p, q) = 1 Γ(α+1) Z ∞ 0 p(x)q(x) x α e −x dx + M p(0)q(0) + N p 0 (0)q 0 (0), N,M ≥ 0, α > −1, firstly introduced by Koekoek and Meijer in 1993 and extensively studied in the last years. We present some new asymptotic properties of these polynomials and also a limit relation between the zeros of these polynomials and the zeros of Bessel function Jα(x). The results are illustrated with numerical examples. Also, some general asymptotic formulas for generalizations of these polynomials are conjectured.
publishDate 2004
dc.date.none.fl_str_mv 2004
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/41725
https://doi.org/10.1016/S0019-3577(04)90012-2
url http://hdl.handle.net/11441/41725
https://doi.org/10.1016/S0019-3577(04)90012-2
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Indagationes Mathematicae, 15 (2), 151-165.
FQM 0262
BFM 2000-0206-C04-02
info:eu-repo/grantAgreement/EC/INTAS-2000-00272/
FQM 0229
BFM 2001-3878-C02-02
http://dx.doi.org/10.1016/S0019-3577(04)90012-2
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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