Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is there any possibility to simplify the following integral or any function that is equivalent to the following integral?

$$ \frac{1}{2\pi\sqrt{(\sigma_{o_x}^2+\sigma_{p_x}^2)(\sigma_{o_y}^2+\sigma_{p_y}^2)}} \int_0^d \int_0^{2\pi} \exp-\bigg[\frac{(r\cos\theta-\alpha_x)^2}{2(\sigma_{o_x}^2+\sigma_{p_x}^2)} + \frac{(r\sin\theta-\alpha_y)^2}{2(\sigma_{o_y}^2+\sigma_{p_y}^2)} \bigg ] r \; d\theta \;dr $$

share|cite|improve this question
1  
I doubt it. You're effecitvely integrating a two-dimensional isotropic normal distribution over an ellipse. – joriki Oct 18 '11 at 7:57
    
I am integrating a 2-dimensional non-isotropic normal function over a circular region. – shaikh Oct 18 '11 at 10:36
    
I know; that's the same thing (through a change of variables). – joriki Oct 18 '11 at 10:49

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.