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Re: A result with Riemann Zeta Function

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  • mikeoakes2
    ... True. This is an immediate consequence of the fact that near s=1, Zeta(s) can be approximated by Zeta(s)=1/(s-1) + EulerGamma + O(|s-1|) See for example
    Message 1 of 2 , Feb 19, 2011
      --- In primenumbers@yahoogroups.com, Sebastian Martin Ruiz <s_m_ruiz@...> wrote:
      >
      > EulerGamma=0.57721566490153286061
      >  
      > Zeta= Riemann Zeta Function
      >  
      > k=constant
      >  
      > We have
      >  
      > Limit a,b->infty   Zeta[a/b]+Zeta[b/a] = 2*EulerGamma -  1
      >   a=/=b   |a-b| <k

      True.

      This is an immediate consequence of the fact that near s=1, Zeta(s) can be approximated by
      Zeta(s)=1/(s-1) + EulerGamma + O(|s-1|)

      See for example Titchmarsh's "Theory of the Riemann Zeta-Function", p.16.

      Mike
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