# Definition:Complementary Error Function

The complementary error function is the real function $\erfc: \R \to \R$:
 $\displaystyle \map {\erfc} x$ $=$ $\displaystyle 1 - \map \erf x$ where $\erf$ denotes the Error Function $\displaystyle$ $=$ $\displaystyle 1 - \dfrac 2 {\sqrt \pi} \int_0^x \map \exp {-t^2} \rd t$ where $\exp$ denotes the Real Exponential Function $\displaystyle$ $=$ $\displaystyle \dfrac 2 {\sqrt \pi} \int_x^\infty \map \exp {-t^2} \rd t$