Hi everyone.(adsbygoogle = window.adsbygoogle || []).push({});

I'm a brazilian mathmatician that didn't studied complex analysis. I study finance and now I'm needing to study that.

In a paper of Lewis (2001) I found an expression that I couldn't understand.

Does anyone can help me with that? They say they use the Residue theorem but I couldn't make the calculations using the versions of this theorem that I found.

The equality is the following:

$ \int_{i Im(u)-\infty} ^{i Im(u)+ \infty} \left( \int_{0} ^{\infty} e^{iuA_t} \Phi^{\ast}(u)dx \right) du=

\pi + 2 \left( \int_{0} ^{\infty} Re \left[ \frac{e^{-iulnK} \Phi^{\ast}(-u) } {iu}\right] du \right) $

(jpg attached for non tex users)

Could you send me reference that I could read and understand the above?

Thanks!

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# Residue Theorem Application

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