# Error function questions

## Main Question or Discussion Point

So i think I'm correct in assuming that the error function is the integral of the function e^(-x^2), but that it can only be expressed in terms of a Taylor series. is it really impossible to express it in terms of elementary functions?

with this same function [e^(-x^2)], how would you integrate it without first converting to a Taylor series and then integrating the summation of the series?

$$ERF(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt$$