- #1
TriTertButoxy
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I'm trying to evaluate the derivative of the Riemann zeta function at the origin, [itex]\zeta'(0)[/itex], starting from its integral representation
[tex]\zeta(s)=\frac{1}{\Gamma(s)}\int_0^\infty t^{s-1}\frac{1}{e^t-1}.[/tex]
I don't want to use a symbolic algebra system like Mathematica or Maple.
I am able to continue to [itex]s=0[/itex] and evaluate the zeta function there [itex]\zeta(0)=-1/2[/itex]. I'm just stuck on how to evaluate the derivative.
Can somebody show me how to do this starting from the integral representation? Thanks.
[tex]\zeta(s)=\frac{1}{\Gamma(s)}\int_0^\infty t^{s-1}\frac{1}{e^t-1}.[/tex]
I don't want to use a symbolic algebra system like Mathematica or Maple.
I am able to continue to [itex]s=0[/itex] and evaluate the zeta function there [itex]\zeta(0)=-1/2[/itex]. I'm just stuck on how to evaluate the derivative.
Can somebody show me how to do this starting from the integral representation? Thanks.