DLMF:25.2.E8 (Q7603): Difference between revisions

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s > 0 𝑠 0 {\displaystyle{\displaystyle\Re s>0}}

\realpart@@{s}>0
Property / constraint: s > 0 𝑠 0 {\displaystyle{\displaystyle\Re s>0}} / rank
 
Normal rank

Revision as of 18:14, 30 December 2019

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DLMF:25.2.E8
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    ζ ( s ) = k = 1 N 1 k s + N 1 - s s - 1 - s N x - x x s + 1 d x , Riemann-zeta 𝑠 superscript subscript 𝑘 1 𝑁 1 superscript 𝑘 𝑠 superscript 𝑁 1 𝑠 𝑠 1 𝑠 superscript subscript 𝑁 𝑥 𝑥 superscript 𝑥 𝑠 1 𝑥 {\displaystyle{\displaystyle\zeta\left(s\right)=\sum_{k=1}^{N}\frac{1}{k^{s}}+% \frac{N^{1-s}}{s-1}-s\int_{N}^{\infty}\frac{x-\left\lfloor x\right\rfloor}{x^{% s+1}}\mathrm{d}x,}}
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    DLMF:25.2.E8
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    s > 0 𝑠 0 {\displaystyle{\displaystyle\Re s>0}}
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