DLMF:25.5.E3 (Q7616)

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DLMF:25.5.E3
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    Statements

    Defining formula
    ζ ⁡ ( s ) = 1 ( 1 - 2 1 - s ) ⁢ Γ ⁡ ( s ) ⁢ ∫ 0 ∞ x s - 1 e x + 1 ⁢ d x , Riemann-zeta 𝑠 1 1 superscript 2 1 𝑠 Euler-Gamma 𝑠 superscript subscript 0 superscript 𝑥 𝑠 1 superscript 𝑒 𝑥 1 𝑥 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{(1-2^{1-s})\Gamma% \left(s\right)}\int_{0}^{\infty}\frac{x^{s-1}}{e^{x}+1}\mathrm{d}x,}}
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    DLMF id
    DLMF:25.5.E3
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    constraint
    ℜ ⁡ s > 0 𝑠 0 {\displaystyle{\displaystyle\Re s>0}}
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