DLMF:25.11.E16 (Q7690)

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DLMF:25.11.E16
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    Defining formula
    ζ ⁡ ( 1 - s , h k ) = 2 ⁢ Γ ⁡ ( s ) ( 2 ⁢ π ⁢ k ) s ⁢ ∑ r = 1 k cos ⁡ ( π ⁢ s 2 - 2 ⁢ π ⁢ r ⁢ h k ) ⁢ ζ ⁡ ( s , r k ) , Hurwitz-zeta 1 𝑠 ℎ 𝑘 2 Euler-Gamma 𝑠 superscript 2 𝜋 𝑘 𝑠 superscript subscript 𝑟 1 𝑘 𝜋 𝑠 2 2 𝜋 𝑟 ℎ 𝑘 Hurwitz-zeta 𝑠 𝑟 𝑘 {\displaystyle{\displaystyle\zeta\left(1-s,\frac{h}{k}\right)=\frac{2\Gamma% \left(s\right)}{(2\pi k)^{s}}\*\sum_{r=1}^{k}\cos\left(\frac{\pi s}{2}-\frac{2% \pi rh}{k}\right)\zeta\left(s,\frac{r}{k}\right),}}
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    DLMF id
    DLMF:25.11.E16
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