Difference between revisions of "Derivative of Riemann zeta"
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Latest revision as of 13:09, 17 September 2016
Theorem
The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \zeta(z) = -\displaystyle\sum_{k=2}^{\infty} \dfrac{\log(k)}{k^z},$$ where $\zeta$ denotes the Riemann zeta and $\log$ denotes the logarithm.
