 Completed Riemann zeta function

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.