First Derivative
\zeta'(s)=-\sum_{n=2}^{\infty}(\log(n))n^{-s}
This formula is a compact form of writing the First Derivative of the Riemann Zeta Function.
Although it’s easy to see that the derivative of the classic definition term for term yields this result, proving that this type of derivation is allowed is non-trivial. Once this equation is clear, the K-th derivative can be simply deduced.
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