Defining a surreal hyperexponential

Vincent Bagayoko (1, 2) , Joris van der Hoeven (3, 2) , Vincenzo Mantova (4)

1 UMons - Université de Mons
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 SFU.ca - Simon Fraser University = Université Simon Fraser
4 School of Mathematics [Leeds]

Conway's class No of surreal numbers admits a rich structure: it forms a totally ordered real closed field with an exponential functions and a derivation. The aim of this note is to construct a surreal solution E to the functional equation E (a + 1) = exp E (a) with good properties.

Domaines: Mathématiques générales [math.GM]; Logique [math.LO]

Vincent Bagayoko, Joris van der Hoeven, Vincenzo Mantova. Defining a surreal hyperexponential. 2020. ⟨hal-02861485v2⟩