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Calculating erf(x)?

by LM741
Tags: erfx
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LM741
#1
Aug10-06, 11:40 AM
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)?

[tex] {erf}(x) = \frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2} dt.[/tex]

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
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HallsofIvy
#2
Aug10-06, 03:21 PM
Math
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PF Gold
P: 39,497
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.
LM741
#3
Aug10-06, 04:32 PM
P: 130
thanks...
by numerical integration do you mean applying Tayler Series and expansions like that?

HallsofIvy
#4
Aug10-06, 08:17 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,497
Calculating erf(x)?

I was thinking more of Simpson's rule.
rbj
#5
Aug10-06, 09:35 PM
P: 2,251
Quote 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.
LM741
#6
Aug11-06, 08:43 AM
P: 130
thanks guys!


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