Error function

In mathematics, the error function is a non-elementary function which occurs in functional analysis. It is defined as:

$\operatorname {erf} (z)={\frac {2}{\sqrt {\pi }}}\int _{0}^{z}e^{-\zeta ^{2}}d\zeta$

It occurs, for example, in solutions of the heat equation when boundary conditions are given by the Heaviside step function.