López García, José LuisPagola Martínez, Pedro JesúsPalacios Herrero, Pablo2024-10-212024-10-212024-08-05López, 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.2024.128987.0096-300310.1016/j.amc.2024.128987https://academica-e.unavarra.es/handle/2454/52340In 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.application/pdfeng© 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC licenseAsymptotic expansions of integralsLaplace's methodSpecial functionsinfo:eu-repo/semantics/article2024-10-21info:eu-repo/semantics/openAccess