Functional Equation for Riemann Zeta Function

Theorem
Let $\zeta$ be the Riemann zeta function.

Let $\zeta(s)$ have an analytic continuation for $\Re(s)>0$.

Then:
 * $\displaystyle \Gamma \left({\frac s 2}\right) \pi^{-s/2} \zeta \left({s}\right) = \Gamma \left({\frac{1-s} 2}\right) \pi^{\frac{s-1} 2} \zeta \left({1-s}\right)$

where $\Gamma$ is the gamma function

Also see

 * Functional Equation for Completed Riemann Zeta Function