Definition:Completed Riemann Zeta Function

Definition
The completed Riemann zeta function is defined to be


 * $\displaystyle \xi(s) = \frac 12 s(s-1) \pi^{-s/2} \Gamma\left(\frac s2\right) \zeta(s)$

on $\Re(s) > 0$, and extended to $\C$ by $\xi(s) = \xi(1-s)$.