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October 17th, 2013, 11:24 AM   #1
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Gaussian integral

Can anyone help with the following integral?



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October 17th, 2013, 12:11 PM   #2
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Re: Gaussian integral

You need to define ? and ?.
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October 17th, 2013, 12:49 PM   #3
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Re: Gaussian integral

The functions in the integrand are PDF and CDF of a standard normal distribution, respectively.
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October 18th, 2013, 12:23 PM   #4
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Re: Gaussian integral

My gut feeling - there is no closed form solution.
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October 18th, 2013, 07:41 PM   #5
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Re: Gaussian integral

I calculated the integral with several problems numerically and obtained solutions. I think a closed form solution may exist. Other similar integrals can be found at http://en.wikipedia.org/wiki/List_of_in ... _functions.
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October 19th, 2013, 12:44 PM   #6
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Re: Gaussian integral

Looking at the reference, it looks like you have two difficulties to overcome. You have an x^2 term (although this probably could be handled) and the limits are (0,?).
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