Formula:8295

Digital Library of Mathematical Functions ID 25.2.E7

${\displaystyle{\displaystyle{\zeta^{(k)}}\left(s\right)=(-1)^{k}\sum_{n=2}^{\infty}(\ln n)^{k}n^{-s},}}$

Constraint(s)

${\displaystyle{\displaystyle\Re s>1}}$
${\displaystyle{\displaystyle\Re s>1}}$
${\displaystyle{\displaystyle k=1,2,3,\dots}}$

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
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle s}}$: complex variable
 

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