- #1

- 194

- 0

[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.