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arXiv · 2509.08473

Taylor expansions over generalised power series

Vincent Bagayoko·Vincenzo Mantova
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Abstract

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 $\omega$-series.

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Vincent Bagayoko, Vincenzo Mantova. 2025-09-10. Taylor expansions over generalised power series. https://arxiv.org/abs/2509.08473

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