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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.

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Journal articles
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https://hal.archives-ouvertes.fr/hal-01389260
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Submitted on : Friday, October 28, 2016 - 11:17:25 AM
Last modification on : Wednesday, October 20, 2021 - 3:18:54 AM

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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, Association des Annales de l'Institut Fourier, 2007, 57 (2), pp.421-456. ⟨10.5802/aif.2263⟩. ⟨hal-01389260⟩

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