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# erfc

Complementary error function

Y = erfc(X)

## Definitions

The complementary error function erfc(X) is defined as

$\begin{array}{c}\text{erfc}\left(x\right)=\frac{2}{\sqrt{\pi }}{\int }_{x}^{\infty }{e}^{-{t}^{2}}dt\\ =1-\text{erf}\left(x\right)\end{array}$

## Description

Y = erfc(X) computes the value of the complementary error function.

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### Tips

The relationship between the complementary error function erfc and the standard normal probability distribution returned by the Statistics Toolbox™ function normcdf is

$\text{normcdf}\left(x\right)=\left(\frac{1}{2}\right)×\text{erfc}\left(\frac{-x}{\sqrt{2}}\right)$