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

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nirovanton
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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

[tex]
\int_0^\infty \theta(v-b)e^{-av^2}dv
[/tex]


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.
 
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Answers and Replies

  • #2
Meir Achuz
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That integral is the error integral [tex](\sqrt{\pi}/2)erfc(b)[/tex].
It must be done numerically or by using a table of erfc or erf.
 

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