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

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