DLMF:25.13.E3 (Q7739)

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DLMF:25.13.E3
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    Statements

    Defining formula
    ζ ⁡ ( 1 - s , x ) = Γ ⁡ ( s ) ( 2 ⁢ π ) s ⁢ ( e - π ⁢ i ⁢ s / 2 ⁢ F ⁡ ( x , s ) + e π ⁢ i ⁢ s / 2 ⁢ F ⁡ ( - x , s ) ) , Hurwitz-zeta 1 𝑠 𝑥 Euler-Gamma 𝑠 superscript 2 𝜋 𝑠 superscript 𝑒 𝜋 𝑖 𝑠 2 periodic-zeta 𝑥 𝑠 superscript 𝑒 𝜋 𝑖 𝑠 2 periodic-zeta 𝑥 𝑠 {\displaystyle{\displaystyle\zeta\left(1-s,x\right)=\frac{\Gamma\left(s\right)% }{(2\pi)^{s}}\left(e^{-\pi is/2}F\left(x,s\right)+e^{\pi is/2}F\left(-x,s% \right)\right),}}
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    DLMF id
    DLMF:25.13.E3
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    constraint
    ℜ ⁡ s > 0 𝑠 0 {\displaystyle{\displaystyle\Re s>0}}
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