# Calculating erf(x)?

by LM741
Tags: erfx
 P: 130 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/ca...9/l2h/img2.png
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,879 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.
 P: 130 thanks... by numerical integration do you mean applying Tayler Series and expansions like that?
Math
Emeritus
Thanks
PF Gold
P: 38,879

## Calculating erf(x)?

I was thinking more of Simpson's rule.
P: 2,265
 Quote by LM741 thanks... by numerical integration do you mean applying Tayler Series and expansions like that?
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.
 P: 130 thanks guys!

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