Formula:DLMF:25.4:E4

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${\displaystyle{\displaystyle{\displaystyle\RiemannXi@{s}=\tfrac{1}{2}s(s-1)\Gamma\left(\tfrac{1}{2}s\right){\pi^{-s/2}}\RiemannZeta@{s}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\xi}}}$ : Riemann's ${\displaystyle{\displaystyle{\displaystyle\RiemannXi}}}$-function : http://dlmf.nist.gov/25.4#E4
${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1
${\displaystyle{\displaystyle{\displaystyle\pi}}}$ : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1

Bibliography

Equation (4), Section 25.4 of DLMF.

URL links

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