DLMF:25.5.E5 (Q7618): Difference between revisions

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Property / constraint
 

- 1 < s < 0 1 𝑠 0 {\displaystyle{\displaystyle-1<\Re s<0}}

-1<\realpart@@{s}<0
Property / constraint: - 1 < s < 0 1 𝑠 0 {\displaystyle{\displaystyle-1<\Re s<0}} / rank
 
Normal rank

Revision as of 17:14, 30 December 2019

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DLMF:25.5.E5
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    Statements

    ζ ( s ) = - s 0 x - x - 1 2 x s + 1 d x , Riemann-zeta 𝑠 𝑠 superscript subscript 0 𝑥 𝑥 1 2 superscript 𝑥 𝑠 1 𝑥 {\displaystyle{\displaystyle\zeta\left(s\right)=-s\int_{0}^{\infty}\frac{x-% \left\lfloor x\right\rfloor-\frac{1}{2}}{x^{s+1}}\mathrm{d}x,}}
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    - 1 < s < 0 1 𝑠 0 {\displaystyle{\displaystyle-1<\Re s<0}}
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