DLMF:25.11.E25 (Q7699)

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DLMF:25.11.E25
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    ζ ( s , a ) = 1 Γ ( s ) 0 x s - 1 e - a x 1 - e - x d x , Hurwitz-zeta 𝑠 𝑎 1 Euler-Gamma 𝑠 superscript subscript 0 superscript 𝑥 𝑠 1 superscript 𝑒 𝑎 𝑥 1 superscript 𝑒 𝑥 𝑥 {\displaystyle{\displaystyle\zeta\left(s,a\right)=\frac{1}{\Gamma\left(s\right% )}\int_{0}^{\infty}\frac{x^{s-1}e^{-ax}}{1-e^{-x}}\mathrm{d}x,}}
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    DLMF:25.11.E25
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    s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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