Error function

Sigmoid shape special function

In mathematics, the error function (also called the Gauss error function), often denoted by e r f {\displaystyle \mathbf {erf} } , is the function erf ⁡ ( z) = 2 π ∫ 0 z e − t 2 d t . {\displaystyle \operatorname {erf} (z)={\frac {2}{\sqrt {\pi }}}\int _{0}^{z}e^{-t^{2}}\,dt.} The integral here is a complex contour integral which is path-independent because exp ⁡ ( − t 2) {\displaystyle \exp(-t^{2})} is holomorphic on the whole complex plane C {\displaystyle \mathbb {C} } . In many applications, the function argument is a real number, in which case the function value is also real.

From Wikipedia, under CC BY-SA. More on occurri.