The hyperserial field of surreal numbers

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

1 UMons - Université de Mons
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 CNRS - Centre National de la Recherche Scientifique

For any ordinal α>0, we show how to define a hyperexponential E_(ω^α) and a hyperlogarithm L_(ω^α) on the class No^(>,≻) of positive infinitely large surreal numbers. Such functions are archetypes of extremely fast and slowly growing functions at infinity. We also show that the surreal numbers form a so-called hyperserial field for our definition.

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

Vincent Bagayoko, Joris van der Hoeven. The hyperserial field of surreal numbers. 2021. ⟨hal-03232836⟩