Formula:DLMF:25.11:E15

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

Constraint(s)

&
&
Failed to parse (unknown function "\realpart"): {\displaystyle {\displaystyle \realpart{a} > 0}}


Proof

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Use

Failed to parse (unknown function "\HurwitzZeta"): {\displaystyle {\displaystyle \HurwitzZeta@{s}{a} = \sum_{n=0}^\infty \frac{1}{(n+a)^s} }}

and analytic continuation.


Symbols List

& : logical and
 : Hurwitz zeta function : http://dlmf.nist.gov/25.11#E1
 : sum : http://drmf.wmflabs.org/wiki/Definition:sum
 : real part : http://dlmf.nist.gov/1.9#E2

Bibliography

Equation (15), Section 25.11 of DLMF.

URL links

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