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Ramanujan Summation

  • Bernard Candelpergher
Chapter
  • 922 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 2185)

Abstract

In the first two sections of this chapter we recall the Euler-MacLaurin formula and use it to define what Ramanujan, in Chapter VI of his second Notebook, calls the “constant” of a series. But, as Hardy has observed, Ramanujan leaves some ambiguity in the definition of this “constant”. Thus in the third section we interpret this constant as the value of a precise solution of a difference equation. Then we can give in Sect. 1.4 a rigorous definition of the Ramanujan summation and its relation to the usual summation for convergent series.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Bernard Candelpergher
    • 1
  1. 1.Laboratoire J.A.Dieudonné. CNRSUniversité de Nice Côte d’ AzurNiceFrance

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