erf() [5/6]

var stan::math::erf ( const var &  a )

inline

The error function for variables (C99).

The derivative is

\(\frac{d}{dx} \mbox{erf}(x) = \frac{2}{\sqrt{\pi}} \exp(-x^2)\).

\[ \mbox{erf}(x) = \begin{cases} \operatorname{erf}(x) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{erf}(x)}{\partial x} = \begin{cases} \frac{\partial\, \operatorname{erf}(x)}{\partial x} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \operatorname{erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2}dt \]

\[ \frac{\partial \, \operatorname{erf}(x)}{\partial x} = \frac{2}{\sqrt{\pi}} e^{-x^2} \]

Parameters

a	The variable.

Returns

Error function applied to the variable.

Definition at line 48 of file erf.hpp.