In mathematics, the complementary error function is a non-elementary function which occurs mainly in probability and statistics.

The complementary error function, denoted erfc, is defined as:

$\backslash mbox\{erfc\}(x)\; =\; \backslash frac\{2\}\{\backslash sqrt\{\backslash pi\}\}\; \backslash int\_x^\{\backslash infty\}\; e^\{-t^2\}\backslash ,dt$

and can also be expressed in terms of the error function:

$\backslash mbox\{erfc\}(x)\; =\; 1\; -\; \backslash mbox\{erf\}(x)$

Special functions