# Ramanujan summation of divergent series

Abstract : In Chapter VI of his second Notebook Ramanujan introduce the Euler-MacLaurin formula to define the " constant " of a series. When the series is divergent he uses this " constant " like a sum of the series. We give a rigorous definition of Ramanujan summation and some properties and applications of it. These properties of the summation seems very unusual so in the last chapter we give a general algebraic view on summation of series that unify Ramanujan summation with the classical summations procedures.
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https://hal.univ-cotedazur.fr/hal-01150208
Contributor : Jean-Louis Thomin <>
Submitted on : Wednesday, March 29, 2017 - 3:20:52 PM
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• HAL Id : hal-01150208, version 2

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B Candelpergher. Ramanujan summation of divergent series. Lectures notes in mathematics, 2185, 2017. ⟨hal-01150208v2⟩

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