Monotonicity and a Taylor approximation theorem for transseries
Vincenzo Mantova
Date: 8 May 2026
Abstract.
We show that the composition of omega-series by surreal numbers, or more generally by elements of any confluent field of transseries, is monotonic in its second argument. In particular, omega-series and LE-series interpreted as functions have the intermediate value property. We also deduce a Taylor approximation theorem for omega-series with maximal radius of validity.
Supported by EPSRC grant EP/T018461/1. For the purpose of open access, the authors has applied a creative commons attribution (CC BY) licence to any author accepted manuscript version arising. No data is associated with the article.
Source: https://arxiv.org/abs/2601.07747. No changes.