Painlevé Property and Generating Functions for Asymptotics
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908717743603712 |
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| author | Kitaev, A. V. |
| author_facet | Kitaev, A. V. |
| contents | This paper proposes a new approach to the asymptotic analysis of Painlevé equations. The approach is based on representing solutions of the Painlevé equations using formal series in two variables, $\sum_{k=0}^{\infty}y^kA_k(x)$, with rational functions $A_k(x)$. The approach is applied to the asymptotic analysis of the third degenerate Painlevé equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14970 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Painlevé Property and Generating Functions for Asymptotics Kitaev, A. V. Classical Analysis and ODEs 33E17, 34M30, 34M35, 34M40, 34M55, 34M56 This paper proposes a new approach to the asymptotic analysis of Painlevé equations. The approach is based on representing solutions of the Painlevé equations using formal series in two variables, $\sum_{k=0}^{\infty}y^kA_k(x)$, with rational functions $A_k(x)$. The approach is applied to the asymptotic analysis of the third degenerate Painlevé equation. |
| title | Painlevé Property and Generating Functions for Asymptotics |
| topic | Classical Analysis and ODEs 33E17, 34M30, 34M35, 34M40, 34M55, 34M56 |
| url | https://arxiv.org/abs/2512.14970 |