DLMF:25.11.E9 (Q7683): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / constraint
 

0 < a 1 0 𝑎 1 {\displaystyle{\displaystyle 0<a\leq 1}}

0<a\leq 1
Property / constraint: 0 < a 1 0 𝑎 1 {\displaystyle{\displaystyle 0<a\leq 1}} / rank
 
Normal rank

Revision as of 18:16, 30 December 2019

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DLMF:25.11.E9
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    Statements

    ζ ( 1 - s , a ) = 2 Γ ( s ) ( 2 π ) s n = 1 1 n s cos ( 1 2 π s - 2 n π a ) , Hurwitz-zeta 1 𝑠 𝑎 2 Euler-Gamma 𝑠 superscript 2 𝜋 𝑠 superscript subscript 𝑛 1 1 superscript 𝑛 𝑠 1 2 𝜋 𝑠 2 𝑛 𝜋 𝑎 {\displaystyle{\displaystyle\zeta\left(1-s,a\right)=\frac{2\Gamma\left(s\right% )}{(2\pi)^{s}}\*\sum_{n=1}^{\infty}\frac{1}{n^{s}}\cos\left(\tfrac{1}{2}\pi s-% 2n\pi a\right),}}
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    DLMF:25.11.E9
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    s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    0 < a 1 0 𝑎 1 {\displaystyle{\displaystyle 0<a\leq 1}}
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