How do I prove that $\zeta'(0)/\zeta(0)=\log(2\pi)$ ?
I can get $\zeta(0)=-\frac{1}{2}$, but I don't know how to calculate $\zeta'(0)=-\frac{1}{2}\log(2\pi)$ ? Can you help me ?
Here $\zeta(s)$ is Riemann zeta function: $\zeta(s):=\sum_{n=1}^{\infty}\frac{1}{n^s}. $