Taylor expansions over generalised power series
Vincent Bagayoko, Vincenzo Mantova
Published: 2025/9/10
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.