Formula:DLMF:25.11:E4

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formula in Hurwitz Zeta Function

Formula:DLMF:25.11:E5 >>

${\displaystyle{\displaystyle{\displaystyle\HurwitzZeta@{s}{a}=\HurwitzZeta@{s}{a+m}+\sum_{n=0}^{m-1}\frac{1}{(n+a)^{s}}}}}$

Constraint(s)

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Hurwitz zeta function : http://dlmf.nist.gov/25.11#E1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum

Bibliography

Equation (4), Section 25.11 of DLMF.

URL links

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formula in Hurwitz Zeta Function

Formula:DLMF:25.11:E5 >>