A convergent version of Watson’s lemma for double integrals

A modification of Watson’s lemma for Laplace transforms ∞ 0 f(t) e−zt dt was introduced in [Nielsen, 1906], deriving a new asymptotic expansion for large |z| with the extra property of being convergent as well. Inspired in that idea, in this paper we derive asymptotic expansions of two-dimensional L...

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Autores: Ferreira González, Chelo, López García, José Luis, Pérez Sinusía, Ester
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/43975
Acceso en línea:https://hdl.handle.net/2454/43975
Access Level:acceso abierto
Palabra clave:Asymptotic expansions of integrals
Watson’s lemma for double integrals
Double Laplace transform
Convergent expansions
Special functions
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spelling A convergent version of Watson’s lemma for double integralsFerreira González, CheloLópez García, José LuisPérez Sinusía, EsterAsymptotic expansions of integralsWatson’s lemma for double integralsDouble Laplace transformConvergent expansionsSpecial functionsA modification of Watson’s lemma for Laplace transforms ∞ 0 f(t) e−zt dt was introduced in [Nielsen, 1906], deriving a new asymptotic expansion for large |z| with the extra property of being convergent as well. Inspired in that idea, in this paper we derive asymptotic expansions of two-dimensional Laplace transforms F(x, y) := ∞ 0 ∞ 0 f(t,s) e−xt−ys dt ds for large |x| and |y| that are also convergent. The expansions of F(x, y) are accompanied by error bounds. Asymptotic and convergent expansions of some specialfunctions are given as illustration.Open access funding provided by Universidad Pública de NavarraTaylor & FrancisEstatistika, Informatika eta MatematikaInstitute for Advanced Materials and Mathematics - INAMAT2Estadística, Informática y MatemáticasUniversidad Pública de Navarra / Nafarroako Unibertsitate Publikoa2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2454/43975reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglés© 2022 The Author(s). This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License, which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/439752026-06-17T12:41:47Z
dc.title.none.fl_str_mv A convergent version of Watson’s lemma for double integrals
title A convergent version of Watson’s lemma for double integrals
spellingShingle A convergent version of Watson’s lemma for double integrals
Ferreira González, Chelo
Asymptotic expansions of integrals
Watson’s lemma for double integrals
Double Laplace transform
Convergent expansions
Special functions
title_short A convergent version of Watson’s lemma for double integrals
title_full A convergent version of Watson’s lemma for double integrals
title_fullStr A convergent version of Watson’s lemma for double integrals
title_full_unstemmed A convergent version of Watson’s lemma for double integrals
title_sort A convergent version of Watson’s lemma for double integrals
dc.creator.none.fl_str_mv Ferreira González, Chelo
López García, José Luis
Pérez Sinusía, Ester
author Ferreira González, Chelo
author_facet Ferreira González, Chelo
López García, José Luis
Pérez Sinusía, Ester
author_role author
author2 López García, José Luis
Pérez Sinusía, Ester
author2_role author
author
dc.contributor.none.fl_str_mv Estatistika, Informatika eta Matematika
Institute for Advanced Materials and Mathematics - INAMAT2
Estadística, Informática y Matemáticas
Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
dc.subject.none.fl_str_mv Asymptotic expansions of integrals
Watson’s lemma for double integrals
Double Laplace transform
Convergent expansions
Special functions
topic Asymptotic expansions of integrals
Watson’s lemma for double integrals
Double Laplace transform
Convergent expansions
Special functions
description A modification of Watson’s lemma for Laplace transforms ∞ 0 f(t) e−zt dt was introduced in [Nielsen, 1906], deriving a new asymptotic expansion for large |z| with the extra property of being convergent as well. Inspired in that idea, in this paper we derive asymptotic expansions of two-dimensional Laplace transforms F(x, y) := ∞ 0 ∞ 0 f(t,s) e−xt−ys dt ds for large |x| and |y| that are also convergent. The expansions of F(x, y) are accompanied by error bounds. Asymptotic and convergent expansions of some specialfunctions are given as illustration.
publishDate 2022
dc.date.none.fl_str_mv 2022
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/2454/43975
url https://hdl.handle.net/2454/43975
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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