Why can't erf be expressed in terms of elementary functions?

Question

I have seen this claim on Wikipedia and other places. Which branch of mathematics does this result come from?

score 6 · Answer 1 · edited Apr 13 '17 at 12:21

6

This is a consequence of the Liouville-Ritt theory of integration in finite terms. You can find a brief sketch and references in my post here.

edited Apr 13 '17 at 12:21

Community

answered Nov 25 '10 at 18:07

Bill Dubuque

score 4 · Answer 2 · answered Nov 25 '10 at 18:06

4

I am not aware of any easy proof of this. Here is a proof that $\int e^{x^2}$ cannot be expressed in terms of elementary functions: http://math.hunter.cuny.edu/ksda/papers/rick_09_02.pdf

answered Nov 25 '10 at 18:06

Timothy Wagner

score 3 · Accepted Answer · answered Nov 25 '10 at 18:04

3

answered Nov 25 '10 at 18:04

Matthew Conroy

3 Answers3