A generalization of the Laplace's method for integrals

Date

2024-08-05

Director

Publisher

Elsevier
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión publicada / Argitaratu den bertsioa

Project identifier

  • AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136441NB-I00/ES/ recolecta
Impacto
OpenAlexGoogle Scholar
No disponible en Scopus

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.

Description

Keywords

Asymptotic expansions of integrals, Laplace's method, Special functions

Department

Institute for Advanced Materials and Mathematics - INAMAT2 / Estadística, Informática y Matemáticas / Estatistika, Informatika eta Matematika

Faculty/School

Degree

Doctorate program

item.page.cita

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.

item.page.rights

© 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC license

Licencia

Los documentos de Academica-e están protegidos por derechos de autor con todos los derechos reservados, a no ser que se indique lo contrario.