How do you do a gaussian integral when it contains a heaviside function?

[nirovanton]

How do you do a gaussian integral when it contains a heaviside function!?

Very few textbooks cover gaussian integrals effectively. This isn't a big deal as they are easy to locate in integral tables, but something I cannot find anywhere is how to handle a gaussian with a heaviside

heaviside = theta

$$\int_0^\infty \theta(v-b)e^{-av^2}dv$$


where b is an arbitrary value of v where the heaviside 'turns on'

If anyone can help shed some light on this for me it would be greatly appreciated.

 

[Meir Achuz]

That integral is the error integral $$(\sqrt{\pi}/2)erfc(b)$$.
It must be done numerically or by using a table of erfc or erf.