functional equation of the Riemann zeta function

Let $\mathrm{\Gamma }$ denote the gamma function, $\zeta$ the Riemann zeta function and $s$ any complex number. Then

${\pi }^{\frac{s-1}{2}}\mathrm{\Gamma }\left({\displaystyle \frac{1-s}{2}}\right)\zeta (1-s)={\pi }^{\frac{-s}{2}}\mathrm{\Gamma }\left({\displaystyle \frac{s}{2}}\right)\zeta (s).$

Though the equation appears too intricate to be of any use, the inherent in the formula makes this the simplest method of evaluating $\zeta (s)$ at points to the left of the critical strip.

Title	functional equation of the Riemann zeta function
Canonical name	FunctionalEquationOfTheRiemannZetaFunction
Date of creation	2013-03-22 13:54:29
Last modified on	2013-03-22 13:54:29
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	6
Author	mathcam (2727)
Entry type	Definition
Classification	msc 11M99
Related topic	ClassNumberFormula