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

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

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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

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