DLMF:25.11.E27 (Q7701): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
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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 18:17, 30 December 2019

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DLMF:25.11.E27
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    ζ ( s , a ) = 1 2 a - s + a 1 - s s - 1 + 1 Γ ( s ) 0 ( 1 e x - 1 - 1 x + 1 2 ) x s - 1 e a x d x , Hurwitz-zeta 𝑠 𝑎 1 2 superscript 𝑎 𝑠 superscript 𝑎 1 𝑠 𝑠 1 1 Euler-Gamma 𝑠 superscript subscript 0 1 superscript 𝑒 𝑥 1 1 𝑥 1 2 superscript 𝑥 𝑠 1 superscript 𝑒 𝑎 𝑥 𝑥 {\displaystyle{\displaystyle\zeta\left(s,a\right)=\frac{1}{2}a^{-s}+\frac{a^{1% -s}}{s-1}+\frac{1}{\Gamma\left(s\right)}\int_{0}^{\infty}\left(\frac{1}{e^{x}-% 1}-\frac{1}{x}+\frac{1}{2}\right)\frac{x^{s-1}}{e^{ax}}\mathrm{d}x,}}
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    DLMF:25.11.E27
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    s > - 1 𝑠 1 {\displaystyle{\displaystyle\Re s>-1}}
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