Definition:Complementary Error Function

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Definition

The complementary error function is the real function $\erfc: \R \to \R$:

\(\displaystyle \map {\erfc} x\) \(=\) \(\displaystyle 1 - \map \erf x\) $\quad$ where $\erf$ denotes the Error Function $\quad$
\(\displaystyle \) \(=\) \(\displaystyle 1 - \dfrac 2 {\sqrt \pi} \int_0^x \map \exp {-t^2} \rd t\) $\quad$ where $\exp$ denotes the Real Exponential Function $\quad$
\(\displaystyle \) \(=\) \(\displaystyle \dfrac 2 {\sqrt \pi} \int_x^\infty \map \exp {-t^2} \rd t\) $\quad$ $\quad$


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