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March 27th, 2008, 06:36 PM   #1
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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
FataLIdea is offline  
 
March 28th, 2008, 05:46 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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