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, B2, B4, B6,... are Bernoulli numbers.

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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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