confusedalot
03-01-05, 02:03 PM
I can't figure out how to prove that the integral from -infinity to +infinity of F(t,w)dw=2(pi)t
where F(t,w)=2(1-cos wt)/w^2
where F(t,w)=2(1-cos wt)/w^2
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View Full Version : Residue Theory Problem confusedalot 03-01-05, 02:03 PM I can't figure out how to prove that the integral from -infinity to +infinity of F(t,w)dw=2(pi)t where F(t,w)=2(1-cos wt)/w^2 James R 03-02-05, 09:06 PM Well, the integrand has a pole at w=0 ... I'd have to revise what I know of contour integration to help you further. Sorry. Maybe somebody else can help. PhysMachine 03-03-05, 12:26 AM You can build up contours around the entire domain of the function. There is a singularity at the origin, which integrates to 2 pi t because you can shrink the entire contour around the singularity by the Cauchy-Goursat theorem. |