arXiv subjects

Yoshiki Kagaya

Publications and source records attributed to Yoshiki Kagaya.

2 recordsLinked to original sources

arXiv2025

Higher-order asymptotic expansion with error estimate for the multidimensional Laplace-type integral under perturbations

We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic expansion with an error estimate, generalizing some previous results including Laplace's method. The key points of the proof are a precise asymptotic analysis based on a lot of detailed Taylor expansions, and a careful consideration of the effects of the perturbations on the Hessian matrix of the phase function.

math.CA↗

arXiv2025

Higher-order asymptotic expansions for Laplace's integral and their error estimates

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.

math.CA↗