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October 17th, 2013, 11:24 AM  #1 
Newbie Joined: Oct 2013 Posts: 3 Thanks: 0  Gaussian integral
Can anyone help with the following integral? Thanks. 
October 17th, 2013, 12:11 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,710 Thanks: 675  Re: Gaussian integral
You need to define ? and ?.

October 17th, 2013, 12:49 PM  #3 
Newbie Joined: Oct 2013 Posts: 3 Thanks: 0  Re: Gaussian integral
The functions in the integrand are PDF and CDF of a standard normal distribution, respectively.

October 18th, 2013, 12:23 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,710 Thanks: 675  Re: Gaussian integral
My gut feeling  there is no closed form solution.

October 18th, 2013, 07:41 PM  #5 
Newbie Joined: Oct 2013 Posts: 3 Thanks: 0  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.

October 19th, 2013, 12:44 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,710 Thanks: 675  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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