DLMF:25.11.E30 (Q7704)

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DLMF:25.11.E30
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    ζ ( s , a ) = Γ ( 1 - s ) 2 π i - ( 0 + ) e a z z s - 1 1 - e z d z , Hurwitz-zeta 𝑠 𝑎 Euler-Gamma 1 𝑠 2 𝜋 𝑖 superscript subscript limit-from 0 superscript 𝑒 𝑎 𝑧 superscript 𝑧 𝑠 1 1 superscript 𝑒 𝑧 𝑧 {\displaystyle{\displaystyle\zeta\left(s,a\right)=\frac{\Gamma\left(1-s\right)% }{2\pi i}\int_{-\infty}^{(0+)}\frac{e^{az}z^{s-1}}{1-e^{z}}\mathrm{d}z,}}
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    DLMF:25.11.E30
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    a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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    s 1 𝑠 1 {\displaystyle{\displaystyle s\neq 1}}
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