Sommation effective d'une somme de Borel par séries de factorielles

Eric Delabaere (1) , Jean-Marc Rasoamanana (1)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

We consider the effective resummation of a Borel sum by its associated factorial series expansion. Our approach provides concrete estimates for the remainder term when truncating this factorial series. We then generalize a theorem of Nevanlinna which gives us the natural framework to extend the factorial series method for Borel-resummable fractional power series expansions.

Mots clés: Borel-resummation; Factorial series

Domaines: Variables complexes [math.CV]

Eric Delabaere, Jean-Marc Rasoamanana. Sommation effective d'une somme de Borel par séries de factorielles. 2006. ⟨hal-00018887⟩