Sommation effective d’une somme de Borel par séries de factorielles / Effective Borel-resummation by factorial series - Archive ouverte HAL Access content directly
Journal Articles Annales de l'Institut Fourier Year : 2007

Sommation effective d’une somme de Borel par séries de factorielles / Effective Borel-resummation by factorial series

Abstract

In this article, 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.

Dates and versions

hal-01389260 , version 1 (28-10-2016)

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Eric Delabaere, Jean-Marc Rasoamanana. Sommation effective d’une somme de Borel par séries de factorielles / Effective Borel-resummation by factorial series. Annales de l'Institut Fourier, 2007, 57 (2), pp.421-456. ⟨10.5802/aif.2263⟩. ⟨hal-01389260⟩
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