# functional equation of the Riemann zeta function

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

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

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 FunctionalEquationOfTheRiemannZetaFunction 2013-03-22 13:54:29 2013-03-22 13:54:29 mathcam (2727) mathcam (2727) 6 mathcam (2727) Definition msc 11M99 ClassNumberFormula