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  • Sebastian Martin Ruiz
    Hello:   I have obtained this interesting limit whit Riemann Zeta function:   Limit {x- 0}
    Message 1 of 2 , Oct 21, 2011
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      Hello:
       
      I have obtained
      this interesting limit whit Riemann Zeta function:
       
      Limit {x->0} (Zeta[2+(x!)^x]-Zeta[3])Log[x]/(x(Zeta[3]-Zeta[2+x^x]))=EulerGamma=0.57721...
       
      I have
      deduced this from: n>=3 positive integer:
       
      Lim
      {x->0} (Zeta[n-1+x^x]-Zeta[n])/(x Log[x])= Sum {k>=1} Log[k]/k^n
       
      And:
       
      Lim
      {x->0} (Zeta[2+(x!)^x]-Zeta[3])/(x^2) = EulerGamma*Sum {k>=1} Log[k]/k^3
       
      I have
      obtained all results using WolframAlpha and MATHEMATICA.
       
      Sincerely:
       
      Sebastián
      Martín Ruiz

      [Non-text portions of this message have been removed]
    • Sebastian Martin Ruiz
      Hello:   I have obtained this interesting limit whit Riemann Zeta function:   Limit {x- 0}
      Message 2 of 2 , Oct 21, 2011
      • 0 Attachment
        Hello:
         
        I have obtained
        this interesting limit whit Riemann Zeta function:
         
        Limit {x->0} (Zeta[2+(x!)^x]-Zeta[3])Log[x]/(x(Zeta[3]-Zeta[2+x^x]))=EulerGamma=0.57721...
         
        I have
        deduced this from: n>=3 positive integer:
         
        Lim
        {x->0} (Zeta[n-1+x^x]-Zeta[n])/(x Log[x])= Sum {k>=1} Log[k]/k^n
         
        And:
         
        Lim
        {x->0} (Zeta[2+(x!)^x]-Zeta[3])/(x^2) = EulerGamma*Sum {k>=1} Log[k]/k^3
         
        I have
        obtained all results using WolframAlpha and MATHEMATICA.
         
        Sincerely:
         
        Sebastián
        Martín Ruiz

        [Non-text portions of this message have been removed]
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