Can the error function be expressed in terms of elementary functions?

[jippetto]

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?

 

[christianjb]

Look at these two pages for more than you ever wanted to know about error functions.

http://en.wikipedia.org/wiki/Error_function
http://mathworld.wolfram.com/Erf.html

Elementary functions are discussed here
http://en.wikipedia.org/wiki/Elementary_function

 

[Gib Z]

And nope, almost but not the integral of the error function.

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