DLMF:25.5.E20 (Q7633)

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DLMF:25.5.E20
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    Statements

    Defining formula
    ζ ⁡ ( s ) = Γ ⁡ ( 1 - s ) 2 ⁢ π ⁢ i ⁢ ∫ - ∞ ( 0 + ) z s - 1 e - z - 1 ⁢ d z , Riemann-zeta 𝑠 Euler-Gamma 1 𝑠 2 𝜋 𝑖 superscript subscript limit-from 0 superscript 𝑧 𝑠 1 superscript 𝑒 𝑧 1 𝑧 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{\Gamma\left(1-s\right)}{% 2\pi i}\int_{-\infty}^{(0+)}\frac{z^{s-1}}{e^{-z}-1}\mathrm{d}z,}}
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    DLMF id
    DLMF:25.5.E20
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    constraint
    s ≠ 1 , 2 , … 𝑠 1 2 … {\displaystyle{\displaystyle s\neq 1,2,\dots}}
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