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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.08473 |
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| _version_ | 1866912580550787072 |
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| author | Bagayoko, Vincent Mantova, Vincenzo |
| author_facet | Bagayoko, Vincent Mantova, Vincenzo |
| contents | We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expansions for fields equipped with a derivation and an exponential function, and apply this to the case of standard fields of transseries, such as $\log$-$\exp$ transseries and $ω$-series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Taylor expansions over generalised power series Bagayoko, Vincent Mantova, Vincenzo Logic Rings and Algebras We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expansions for fields equipped with a derivation and an exponential function, and apply this to the case of standard fields of transseries, such as $\log$-$\exp$ transseries and $ω$-series. |
| title | Taylor expansions over generalised power series |
| topic | Logic Rings and Algebras |
| url | https://arxiv.org/abs/2509.08473 |