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 March 27th, 2008, 05:36 PM #1 Newbie   Joined: Mar 2008 Posts: 1 Thanks: 0 Integration of Gaussian Surface Hello, first time posting here. We all know the nice way to integrate y = exp(-ar^2) using polar coordinates, right? What about y = exp(-r^2/(2*(a+bsin(n*theta - phi))^2) Obviously I am trying to make the denominator in the exponential argument look similar to the standard deviation (sigma) of the standard Gaussian y = exp(-r^2/(2*sigma^2)). Perhaps I should write the sinusoid term in the numerator (similar to the ar^2)? If anyone knows how to get the normalization factor for this form of Gaussian, that'd be great to see! Cheers
March 28th, 2008, 04:46 PM   #2
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Re: Integration of Gaussian Surface

Quote:
 Originally Posted by FataLIdea Hello, first time posting here. We all know the nice way to integrate y = exp(-ar^2) using polar coordinates, right? What about y = exp(-r^2/(2*(a+bsin(n*theta - phi))^2) Obviously I am trying to make the denominator in the exponential argument look similar to the standard deviation (sigma) of the standard Gaussian y = exp(-r^2/(2*sigma^2)). Perhaps I should write the sinusoid term in the numerator (similar to the ar^2)? If anyone knows how to get the normalization factor for this form of Gaussian, that'd be great to see! Cheers
If the expressions dviding r^2 are independent of r, you don't have a problem.

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