Symbols:E/Complementary Error Function

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Complementary Error Function

$\erfc$

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

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


Its $\LaTeX$ code is erfc .