Formula:8717

Digital Library of Mathematical Functions ID 27.4.E13

${\displaystyle{\displaystyle\sum_{n=2}^{\infty}(\ln n)n^{-s}=-\zeta'\left(s\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re s>1}}$

Symbols List

• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle n}}$: positive integer
 

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