I have a doubt on this following procedure using the residue theorem:(adsbygoogle = window.adsbygoogle || []).push({});

Initially we have

ψ(k,t)=[itex]\frac{1}{2\pi}\int_{L_{\omega}}\frac{S(k,\omega)}{D(k,\omega)}e^{-i\omega t}d\omega[/itex]

Then the author said using the residue theorem, we have

ψ(k,t)=[itex]-iƩ_{j}\frac{S(k,\omega_j(k))}{\partial D/ \partial \omega (k,\omega_j(k))}e^{-i\omega_j(k) t}[/itex]

where [itex]S(k,\omega_j(k)), D(k,\omega_j(k))[/itex] are functions relating [itex]k[/itex] and [itex]\omega[/itex].

What kind of residue theorem is the author using?

Thank you very much

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# The residue theorem

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