DLMF:25.5.E11 (Q7624): 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.m2ajdec

Revision as of 12:26, 2 January 2020

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DLMF:25.5.E11
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    ζ ( s ) = 1 2 + 1 s - 1 + 2 0 sin ( s arctan x ) ( 1 + x 2 ) s / 2 ( e 2 π x - 1 ) d x . Riemann-zeta 𝑠 1 2 1 𝑠 1 2 superscript subscript 0 𝑠 𝑥 superscript 1 superscript 𝑥 2 𝑠 2 superscript 𝑒 2 𝜋 𝑥 1 𝑥 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{2}+\frac{1}{s-1}+2% \int_{0}^{\infty}\frac{\sin\left(s\operatorname{arctan}x\right)}{(1+x^{2})^{s/% 2}(e^{2\pi x}-1)}\mathrm{d}x.}}
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    ζ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    C25.S2.E1.m2ajdec
    0 references