Explicit error term of the elliptic asymptotics for the first Painlevé transcendents
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910601887875072 |
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| author | Shimomura, Shun |
| author_facet | Shimomura, Shun |
| contents | For the first Painlevé transcendents Kitaev established an asymptotic representation in terms of the Weierstrass pe-function in cheese-like strips near the point at infinity. We present an explicit error bound of this asymptotic expression, which leads to the order estimate of exponent $-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14639 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Explicit error term of the elliptic asymptotics for the first Painlevé transcendents Shimomura, Shun Classical Analysis and ODEs 34M55, 34M56, 34M40, 34M60, 33E05 For the first Painlevé transcendents Kitaev established an asymptotic representation in terms of the Weierstrass pe-function in cheese-like strips near the point at infinity. We present an explicit error bound of this asymptotic expression, which leads to the order estimate of exponent $-1$. |
| title | Explicit error term of the elliptic asymptotics for the first Painlevé transcendents |
| topic | Classical Analysis and ODEs 34M55, 34M56, 34M40, 34M60, 33E05 |
| url | https://arxiv.org/abs/2307.14639 |