Functional equation for Riemann zeta

Theorem

The following formula holds for all $z \in \mathbb{C}$: $$\zeta(z)=2^z \pi^{z-1} \sin \left( \dfrac{\pi z}{2} \right) \Gamma(1-z)\zeta(1-z),$$ where $\zeta$ denotes Riemann zeta, $\pi$ denotes pi, $\sin$ denotes sine, and $\Gamma$ denotes gamma.

References

• 1930: Edward Charles Titchmarsh: The Zeta-Function of Riemann ... (previous) ... (next): § Introduction $(6)$