Formula:8391

Digital Library of Mathematical Functions ID 25.11.E24

${\displaystyle{\displaystyle\sum_{r=1}^{k-1}\zeta'\left(s,\frac{r}{k}\right)=(k^{s}-1)\zeta'\left(s\right)+k^{s}\zeta\left(s\right)\ln k,}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$: Hurwitz zeta function
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
• ${\displaystyle{\displaystyle s}}$: complex variable
• ${\displaystyle{\displaystyle k}}$: integer
 

Resources that cite this formula

No records found.