Higher-order asymptotic expansions for Laplace's integral and their error estimates
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915272213921792 |
|---|---|
| author | Fukuda, Ikki Kagaya, Yoshiki |
| author_facet | Fukuda, Ikki Kagaya, Yoshiki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00801 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-order asymptotic expansions for Laplace's integral and their error estimates Fukuda, Ikki Kagaya, Yoshiki Classical Analysis and ODEs 41A60, 41A80 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. |
| title | Higher-order asymptotic expansions for Laplace's integral and their error estimates |
| topic | Classical Analysis and ODEs 41A60, 41A80 |
| url | https://arxiv.org/abs/2504.00801 |