Functional equation of the Riemann zeta function
= Functional equation of the Riemann zeta function
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{wiki=Riemann_zeta_function#Riemann's_functional_equation}
The completed zeta function
$$
\xi(s)=\frac12s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s)
$$
is an <entire function> satisfying $\xi(s)=\xi(1-s)$. Thus every nontrivial zero $\rho$ is accompanied by $1-\rho$, $\overline\rho$, and $1-\overline\rho$.