# Just an integral...

by botee
Tags: correlation, fourier, integral
 P: 12 Hi everyone! Could someone help me with evaluating the following integral? $\int_{2 \pi /L}^{\pi/l_0} \int_{2 \pi /L}^{\pi/l_0} \frac{\cos(k_x \Delta x)}{k_x^2 + k_y^2} dk_x dk_y$ I have a good reason to believe that it will end up with some $\frac{1}{2} \ln (\frac{L}{\Delta x})$ though this might just be some approximation of it, since $l_0 \ll L, \Delta x \ll L$ . Any help would be appreciated! Thank you!