Formula:8382

Digital Library of Mathematical Functions ID 25.11.E15

${\displaystyle{\displaystyle\zeta\left(s,ka\right)=k^{-s}\*\sum_{n=0}^{k-1}\zeta\left(s,a+\frac{n}{k}\right),}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$: Hurwitz zeta function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
• ${\displaystyle{\displaystyle s}}$: complex variable
 

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