$$\operatorname{erf} \left( x \right) = \frac{2}{{\sqrt \pi }}\int\limits_0^x {{e^{ - {t^2}}}dt} = \frac{2}{{\sqrt \pi }}\sum\limits_{n = 0}^{ + \infty } {\frac{{{{\left( { - 1} \right)}^n}{x^{2n + 1}}}}{{n!\left( {2n + 1} \right)}}} $$