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Archiv der Mathematik

, Volume 74, Issue 3, pp 207–211 | Cite as

Sharp bounds for the Bernoulli numbers

  • H. Alzer

Abstract.

We determine the best possible real constants \(\alpha\) and \(\beta\) such that the inequalities \({2(2n)! \over(2\pi)^{2n}} {1 \over 1-2^{\alpha -2n}} \leqq |B_{2n}| \leqq {2(2n)! \over (2\pi )^{2n}}\, {1 \over 1-2^{\beta -2n}}\)hold for all integers \(n\geqq 1\). Here, B 2, B 4, B 6,... are Bernoulli numbers.

Keywords

Real Constant Sharp Bound Bernoulli Number 
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 2000

Authors and Affiliations

  • H. Alzer
    • 1
  1. 1.Morsbacher Str. 10, 51545 Waldbröl, GermanyDE

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