Inverse Fourier Transform

[fannushofi]

I want to ask you how to calculate the Inverse Fourier Transform (IFT) of

where,

so the IFT is,

assume that

. So,

from here I can't go further, because I have trouble how to integrate that function with the limitation.
Anyone can help me??

Thx

 

[chiro]

Hey fannushofi.

Hint: Look at the Gamma integral but adjust it for a complex argument.