Difference between revisions of "Functional equation for Riemann zeta"
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Latest revision as of 00:00, 18 March 2017
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.
Proof
References
- 1930: Edward Charles Titchmarsh: The Zeta-Function of Riemann ... (previous) ... (next): § Introduction $(6)$
