Formula:DLMF:25.11:E24

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Failed to parse (unknown function "\hiderel"): {\displaystyle {\displaystyle \sum_{r \hiderel{=} 1}^{k-1} \HurwitzZeta'@{s}{\frac{r}{k}} = (k^s - 1) \RiemannZeta'@{s} + k^s \RiemannZeta@{s} \ln@@{k} }}

Constraint(s)

&


Note(s)

primes on Failed to parse (unknown function "\HurwitzZeta"): {\displaystyle {\displaystyle \HurwitzZeta}} denote derivatives with respect to


Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Use

Failed to parse (unknown function "\HurwitzZeta"): {\displaystyle {\displaystyle \HurwitzZeta@{s}{ka} = k^{-s} \* \sum_{n=0}^{k-1} \HurwitzZeta@{s}{a+\frac{n}{k}} }}
with ,

multiply by and differentiate.


Symbols List

& : logical and
 : sum : http://drmf.wmflabs.org/wiki/Definition:sum
 : Hurwitz zeta function : http://dlmf.nist.gov/25.11#E1
 : Riemann zeta function : http://dlmf.nist.gov/25.2#E1
 : principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2

Bibliography

Equation (24), Section 25.11 of DLMF.

URL links

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