Completed Riemann zeta function
= Completed Riemann zeta function
{title2=$\Lambda(s)=\pi^{-s/2}\Gamma(s/2)\zeta(s)$}
The completed zeta function $\Lambda(s)=\pi^{-s/2}\Gamma(s/2)\zeta(s)$ satisfies $\Lambda(s)=\Lambda(1-s)$ and has poles at zero and one. It is also sometimes denoted $\xi(s)$; this differs from the entire xi function obtained by multiplying by $s(s-1)/2$. The distinction matters in the <constant term of a nonholomorphic Eisenstein series>.