Error function

• March 18th 2009, 04:18 PM
math2009
Error function
Could anybody know formulation of integration

$f(x)=\int _0 ^x e^{-t^2}dt$

Formulation is not series.
• March 18th 2009, 06:01 PM
matheagle
you cannot integrate this, unless you let x go to infinity.
However you can approximate it via it's Taylor Series
• March 18th 2009, 06:39 PM
math2009
I try to solve it, and get a approximate formulation

$\int _0 ^x e^{-t^2}dt \approx \frac{\sqrt{\pi (1-e^{-x^2})}}{2}$

There is small error when x < 3
I believe it must have precision formulation
• March 18th 2009, 06:43 PM
mr fantastic
Quote:

Originally Posted by math2009
I try to solve it, and get a approximate formulation

$\int _0 ^x e^{-t^2}dt \approx \frac{\sqrt{\pi (1-e^{-x^2})}}{2}$

I believe it must have precision formulation

It doesn't. Read this: Integration of Nonelementary Functions
• March 18th 2009, 07:06 PM
math2009
If k = 1.24 , then
$\int _0 ^x e^{-t^2}dt \approx \frac{\sqrt{\pi (1-e^{-kx^2})}}{2}$

It will approach very small error.
Could you find k or k(x) to minimum error ?
If we let limit of error to 0, it mean we get formulation

As your claim, "There are two things you should never try to prove ...... the impossible and the obvious."
You never prove it doesn't.