A generalization of the Laplace's method for integrals
| dc.contributor.author | López García, José Luis | |
| dc.contributor.author | Pagola Martínez, Pedro Jesús | |
| dc.contributor.author | Palacios Herrero, Pablo | |
| dc.contributor.department | Institute for Advanced Materials and Mathematics - INAMAT2 | en |
| dc.contributor.department | Estadística, Informática y Matemáticas | es_ES |
| dc.contributor.department | Estatistika, Informatika eta Matematika | eu |
| dc.contributor.funder | Universidad Publica de Navarra / Nafarroako Unibertsitate Publikoa | |
| dc.date.accessioned | 2024-10-21T14:56:50Z | |
| dc.date.available | 2024-10-21T14:56:50Z | |
| dc.date.issued | 2024-08-05 | |
| dc.date.updated | 2024-10-21T14:46:26Z | |
| dc.description.abstract | In López, Pagola and Perez (2009) we introduced a modification of the Laplace's method for deriving asymptotic expansions of Laplace integrals which simplifies the computations, giving explicit formulas for the coefficients of the expansion. On the other hand, motivated by the approximation of special functions with two asymptotic parameters, Nemes has generalized Laplace's method by considering Laplace integrals with two asymptotic parameters of a different asymptotic order. Nemes considers a linear dependence of the phase function on the two asymptotic parameters. In this paper, we investigate if the simplifying ideas introduced in López, Pagola and Perez (2009) for Laplace integrals with one large parameter may be also applied to the more general Laplace integrals considered in Nemes's theory. We show in this paper that the answer is yes, but moreover, we show that those simplifying ideas can be applied to more general Laplace integrals where the phase function depends on the large variable in a more general way, not necessarily in a linear form. We derive new asymptotic expansions for this more general kind of integrals with simple and explicit formulas for the coefficients of the expansion. Our theory can be applied to special functions with two or more large parameters of a different asymptotic order. We give some examples of special functions that illustrate the theory. | en |
| dc.description.sponsorship | The Universidad Pública de Navarra, plan de promoción de grupos de investigación, and the Ministerio de Ciencia, Innovación y Universidades, project PID2022-136441NB-I00, are acknowledged by their financial support. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | López, J. L., Pagola, P. J., Palacios, P. (2024) A generalization of the Laplace's method for integrals. Applied Mathematics and Computation, 483(15), 1-20. https://doi.org/10.1016/j.amc.2024.128987. | |
| dc.identifier.doi | 10.1016/j.amc.2024.128987 | |
| dc.identifier.issn | 0096-3003 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/52340 | |
| dc.language.iso | eng | |
| dc.publisher | Elsevier | |
| dc.relation.ispartof | Applied Mathematics and Computation 483, 2024, 128987 | |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136441NB-I00/ES/ | |
| dc.relation.publisherversion | https://doi.org/10.1016/j.amc.2024.128987 | |
| dc.rights | © 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC license | |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc/4.0/ | |
| dc.subject | Asymptotic expansions of integrals | en |
| dc.subject | Laplace's method | en |
| dc.subject | Special functions | en |
| dc.title | A generalization of the Laplace's method for integrals | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/publishedVersion | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | e6cd33c5-6d5e-455c-b8da-32a9702e16c8 | |
| relation.isAuthorOfPublication | 68ff8840-f80e-4119-ac1a-edfad578de07 | |
| relation.isAuthorOfPublication | 8793d0db-cf29-4d69-96be-387a3677fc64 | |
| relation.isAuthorOfPublication.latestForDiscovery | e6cd33c5-6d5e-455c-b8da-32a9702e16c8 |