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Archiv der Mathematik

, Volume 71, Issue 1, pp 22–30 | Cite as

On a queer binomial sum

  • Robert Denk
  • Richard Warlimont
  • 30 Downloads

Abstract.

In this paper the binomial sum¶¶\( S_n(r) = \sum \limits_{m=0}^n {n\choose m} {{(-1)^m} \over {m^r+1}} (r \ge 0,\; n \in {\Bbb N})\)¶¶is investigated. It turns out that the behaviour of this sum for \( n\to \infty \) depends on the parameter r and changes dramatically at the values r = 1 and r = 2. In particular, for \( r\ge 2 \) we obtain an oscillatory behaviour while for \( r \le 2 \) the sequence S n (r) is monotonous at least for large values of n.

Keywords

Oscillatory Behaviour 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • Robert Denk
    • 1
  • Richard Warlimont
    • 1
  1. 1.NWF I – Mathematik, Universität Regensburg, D-93040 Regensburg, GermanyDE

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