I have got the below fourier problem:
The Fourier transform of a function is defined as:
I have worked through it and got two different answers depending on whether I used a positive contour or negative contour.
For the positive contour:
For the negative contour:
I'm not sure whether these need to be combined or which one to use for the final answer. Looked at Wolfram Alpha and this gave something completely different.
Can someone please point me in the right direction.
Think about which way you traverse the two contours and what that means for the part of the integral along the real axis, also which contour you use depends on the sign of to make the integral over the semicircular arc go to zero, see the very similar problem on the Wikipedia page.
CB