Formula:DLMF:25.4:E1

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formula in Reflection Formulas

Formula:DLMF:25.4:E2 >>

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

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle s\neq 0,1}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1
${\displaystyle{\displaystyle{\displaystyle\pi}}}$ : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}}}}$ : cosine function : http://dlmf.nist.gov/4.14#E2
${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1

Bibliography

Equation (1), Section 25.4 of DLMF.

URL links

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formula in Reflection Formulas

Formula:DLMF:25.4:E2 >>