DLMF:25.5.E6 (Q7619)

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DLMF:25.5.E6
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    Statements

    test
    ζ ⁡ ( s ) = 1 2 + 1 s - 1 + 1 Γ ⁡ ( s ) ⁢ ∫ 0 ∞ ( 1 e x - 1 - 1 x + 1 2 ) ⁢ x s - 1 e x ⁢ d x , Riemann-zeta 𝑠 1 2 1 𝑠 1 1 Euler-Gamma 𝑠 superscript subscript 0 1 superscript 𝑒 𝑥 1 1 𝑥 1 2 superscript 𝑥 𝑠 1 superscript 𝑒 𝑥 𝑥 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{2}+\frac{1}{s-1}+% \frac{1}{\Gamma\left(s\right)}\int_{0}^{\infty}\left(\frac{1}{e^{x}-1}-\frac{1% }{x}+\frac{1}{2}\right)\frac{x^{s-1}}{e^{x}}\mathrm{d}x,}}
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    DLMF id
    DLMF:25.5.E6
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    constraint
    ℜ ⁡ s > - 1 𝑠 1 {\displaystyle{\displaystyle\Re s>-1}}
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