Higher-order asymptotic expansions for Laplace's integral and their error estimates
Classical Analysis and ODEs
2025-05-06 v2
Abstract
We deal with the asymptotic analysis for Laplace's integral. For this problem, the so-called Laplace's method by P.S. Laplace (1812) is well-known and it has been developed in various forms over many years of studies. In this paper, we derive some formulas of the higher-order asymptotic expansions for that integral, with error estimates, which generalize previous results. Moreover, we discuss a comparison of these asymptotic formulas with approximations using numerical integral.
Keywords
Cite
@article{arxiv.2504.00801,
title = {Higher-order asymptotic expansions for Laplace's integral and their error estimates},
author = {Ikki Fukuda and Yoshiki Kagaya},
journal= {arXiv preprint arXiv:2504.00801},
year = {2025}
}
Comments
7 pages. This version includes some corrections to the original paper