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math.CA2025
Higher-order asymptotic expansions for Laplace's integral and their error estimates
Ikki Fukuda, Yoshiki Kagaya
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 vari…
math.CA2025
Higher-order asymptotic expansion with error estimate for the multidimensional Laplace-type integral under perturbations
Ikki Fukuda, Yoshiki Kagaya, Yuki Ueda
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 e…