For $\mathrm{Re}(s)>-1$, $$-\zeta'(s)=\lim_{N\rightarrow{\infty}} -\frac{N^{1-s}\log N}{1-s}+\frac{N^{1-s}}{(1-s)^2}-\frac{1}{2}N^{-s}\log N+\sum_{n=1}^N \log(n)n^{-s}.$$ Please give me the proof of this formula.
2026-04-10 09:26:04.1775813164
An integral representation of Riemann zeta function
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