# Calculating a complex integral

#### Robin04

Problem Statement
$f(\omega)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}dt \ e^{-\frac{t^2}{2\sigma^2}+t(i\omega-\alpha)}cos(\Omega t)$
Relevant Equations
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As this function has no singularities the residue theorem cannot be applied. Can you help me a bit?

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#### vela

Staff Emeritus
Homework Helper
Looks like you can express it in terms of the Fourier transform of a Gaussian.

"Calculating a complex integral"

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