DLMF:25.5.E16 (Q7629): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Riemann zeta function / rank
 
Normal rank
Property / Symbols used: Riemann zeta function / qualifier
 
test:

ζ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}

\Riemannzeta@{\NVar{s}}
Property / Symbols used: Riemann zeta function / qualifier
 
xml-id: C25.S2.E1.m2andec

Revision as of 12:28, 2 January 2020

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DLMF:25.5.E16
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    ζ ( s ) = 1 s - 1 + sin ( π s ) π ( s - 1 ) 0 ( 1 1 + x - ψ ( 1 + x ) ) x 1 - s d x , Riemann-zeta 𝑠 1 𝑠 1 𝜋 𝑠 𝜋 𝑠 1 superscript subscript 0 1 1 𝑥 diffop digamma 1 1 𝑥 superscript 𝑥 1 𝑠 𝑥 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{s-1}+\frac{\sin\left(% \pi s\right)}{\pi(s-1)}\*\int_{0}^{\infty}\left(\frac{1}{1+x}-\psi'\left(1+x% \right)\right)x^{1-s}\mathrm{d}x,}}
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    ζ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    C25.S2.E1.m2andec
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