DLMF:25.5.E16 (Q7629)

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DLMF:25.5.E16
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    ζ ⁡ ( s ) = 1 s - 1 + sin ⁡ ( π ⁢ s ) π ⁢ ( s - 1 ) ⁢ ∫ 0 ∞ ( 1 1 + x - ψ ′ ⁡ ( 1 + x ) ) ⁢ x 1 - s ⁢ d x , Riemann-zeta 𝑠 1 𝑠 1 𝜋 𝑠 𝜋 𝑠 1 superscript subscript 0 1 1 𝑥 diffop digamma 1 1 𝑥 superscript 𝑥 1 𝑠 𝑥 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{s-1}+\frac{\sin\left(% \pi s\right)}{\pi(s-1)}\*\int_{0}^{\infty}\left(\frac{1}{1+x}-\psi'\left(1+x% \right)\right)x^{1-s}\mathrm{d}x,}}
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    DLMF id
    DLMF:25.5.E16
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