Difference between revisions of "Functional equation for Riemann zeta"

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(Created page with "==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 $\zeta$ denote...")
 
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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