Indefinite Integral

Erienion

I've been trying to integrate the following function but have gotten somewhat stuck doing it. The answer i managed to produce gave some bogan answers.

the integral in question is

[tex]\int e^\frac{-(x-\mu)^2}{(2\sigma)^2}[/tex]

where [tex]\mu[/tex] and [tex]\sigma[/tex] are constants.

its part of the normal equation and ive been trying to write a program to do some calculations with it.

Tide

The integral can be expressed in terms of the error function, erf(x). Unfortunately, there is no elementary form.

quasar987

As far as I can see, by setting [itex]y = x-\mu /2\sigma[/itex], we get the famous [itex]e^{-y^2}[/itex] which doesn't have a primitive. You can however develop [itex]e^{-y^2}[/itex] as a Taylor serie and integrate term by term. You get the (convergant) serie of general term

[tex]a_n=\frac{(-1)^n x^{2n+1}}{(2n + 1)n!}[/tex]