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I'm trying to evaluate the integral of a function

$$\frac{\psi_m^T\cdot P\cdot\phi_m\cdot\exp(-\gamma\xi i)}{(\gamma_m-\gamma)\cdot B_m}$$

with respect to $\gamma$, where $\psi_m$ is a $1\times n$ row vector, P is a $n\times n$ matrix, $\phi_m$ is a $1\times n$ row vector and $B_m$ is a constant. This integral comes from the inverse Fourier transform application and, as it can be seen, there are $n$ singularities on the known values $\gamma_m$. Some of these singularities are pure real values, others are pure imaginary and some have the form $a+b*i$.

My question is: I want to calculate the integral using the residue theorem. Should I use all the singularities of the integrand? And if so, how should I manipulate the complex singularities?

Any help would be valuable!

Thanks,

Antigoni

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Pedro
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Antigoni B
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    Use LaTeX to write mathematics in this site, otherwise it's hard to understand what you meant. – DonAntonio Jul 22 '13 at 19:40
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    I have edited. Is the edit what you intended? – Pedro Jul 22 '13 at 19:41
  • I'm sorry, but I don't have LaTeX. Unfortunately, I can't upload any picture, since I'm a new user. Is there another way to make it more clear what I mean? – Antigoni B Jul 22 '13 at 19:51
  • Yes Peter. This is what I mean. Thanks a lot! Although there is an integral symbol in front of the function from -Infinity to +Infinity. I suppose you can see the integral at the end of my question, as well as the function before the inverse fourier application (V with 'hat') – Antigoni B Jul 22 '13 at 19:53

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