# Calculating erf(x)?

1. Aug 10, 2006

### LM741

Hi guys...
don't suppose anybody knows how to calculate the error function - erf(x)

I know Matlab can calculate it - but is it possible to evaluate it without computational techniques (i.e. using computers)?

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

Would appreciate any feedback.

thanks.

The link below will direct you to a website where the equation can be viewed...

http://images.planetmath.org:8080/cache/objects/6429/l2h/img2.png

Last edited by a moderator: Aug 10, 2006
2. Aug 10, 2006

### HallsofIvy

Staff Emeritus
If you mean "Is there an elementary anti-derivative" that can be evaluated directly, the answer is no. The only way to evaluate erf(x) is to do a numerical integration.

3. Aug 10, 2006

### LM741

thanks...
by numerical integration do you mean applying Tayler Series and expansions like that?

4. Aug 10, 2006

### HallsofIvy

Staff Emeritus
I was thinking more of Simpson's rule.

5. Aug 10, 2006

### rbj

actually, with a computer program to calculate the terms and summation, that is what they do. one thing is that there is a nice closed form expression for the erf(x) for large x.

see http://mathworld.wolfram.com/Erf.html for some detail.

6. Aug 11, 2006

thanks guys!