Formula:DLMF:25.4:E2

<< Formula:DLMF:25.4:E1

formula in Reflection Formulas

Formula:DLMF:25.4:E3 >>

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

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

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
${\displaystyle{\displaystyle{\displaystyle\mathrm{sin}}}}$ : sine function : http://dlmf.nist.gov/4.14#E1
${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1

Bibliography

Equation (2), Section 25.4 of DLMF.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:DLMF:25.4:E1

formula in Reflection Formulas

Formula:DLMF:25.4:E3 >>