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Possible Duplicate:
complex integration over the whole plane

I am trying to solve the integral $\int_{\mathbb{C}}f(|z|^2)dz$. I have seen the final results in a paper but do not know how to evaluate it. Specifically, the integrand is only analytic in limited number of points in complex plan, so how one can perform the integration with a unique answer over the whole plane? Thanks for all the help.

Newly Edited

$f(z) = \sum_{x_1}\sum_{x_2}\exp{(-|z-(ax_1+bx_2)|^2})\log_2\sum_{x_1}\sum_{x_2}\exp(-|z-(ax_1+bx_2)|^2)$

where $a,b$ are real positive numbers, and $x_1,x_2$ are complex numbers (on a grid of integer points) in 2D plane. The integration is meant to be taken over the whole plane. Can't figure out how it should be done. Either it is possible to 2D integration or must be evaluated using complex analysis.

Please see this link. It wasn't possible that I merge this post to my profile. That made me to write a better question. Sorry I don't know much about this site options (either I should comment or write this edit as answer etc.) Thank you.

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    @Willie Wong: Thank you!2012-09-12

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