DLMF:25.5.E8 (Q7621): Difference between revisions

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s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}

\realpart@@{s}>1
Property / constraint: s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}} / rank
 
Normal rank

Revision as of 18:14, 30 December 2019

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DLMF:25.5.E8
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    ζ ( s ) = 1 2 ( 1 - 2 - s ) Γ ( s ) 0 x s - 1 sinh x d x , Riemann-zeta 𝑠 1 2 1 superscript 2 𝑠 Euler-Gamma 𝑠 superscript subscript 0 superscript 𝑥 𝑠 1 𝑥 𝑥 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{2(1-2^{-s})\Gamma% \left(s\right)}\int_{0}^{\infty}\frac{x^{s-1}}{\sinh x}\mathrm{d}x,}}
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    DLMF:25.5.E8
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    s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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