Functional equation for Riemann zeta with cosine

Theorem

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

References

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