DLMF:25.13.E3 (Q7739): Difference between revisions

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

0 < x < 1 0 𝑥 1 {\displaystyle{\displaystyle 0<x<1}}

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

Revision as of 18:18, 30 December 2019

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DLMF:25.13.E3
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    Statements

    ζ ( 1 - s , x ) = Γ ( s ) ( 2 π ) s ( e - π i s / 2 F ( x , s ) + e π i s / 2 F ( - x , s ) ) , Hurwitz-zeta 1 𝑠 𝑥 Euler-Gamma 𝑠 superscript 2 𝜋 𝑠 superscript 𝑒 𝜋 𝑖 𝑠 2 periodic-zeta 𝑥 𝑠 superscript 𝑒 𝜋 𝑖 𝑠 2 periodic-zeta 𝑥 𝑠 {\displaystyle{\displaystyle\zeta\left(1-s,x\right)=\frac{\Gamma\left(s\right)% }{(2\pi)^{s}}\left(e^{-\pi is/2}F\left(x,s\right)+e^{\pi is/2}F\left(-x,s% \right)\right),}}
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    DLMF:25.13.E3
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    s > 0 𝑠 0 {\displaystyle{\displaystyle\Re s>0}}
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    0 < x < 1 0 𝑥 1 {\displaystyle{\displaystyle 0<x<1}}
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