Calculating a complex integral

Thread starter Robin04
Start date May 16, 2019
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Complex Complex integral Integral

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The discussion centers on calculating a complex integral that lacks singularities, making the residue theorem inapplicable. Participants suggest expressing the integral using the Fourier transform of a Gaussian function. This approach may simplify the computation and provide a clearer pathway to the solution. The conversation emphasizes the importance of alternative methods in complex analysis when traditional techniques are not viable. Overall, the focus remains on finding effective strategies for evaluating the integral.

May 16, 2019

Robin04

Homework 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: -

As this function has no singularities the residue theorem cannot be applied. Can you help me a bit?

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May 16, 2019

vela

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Looks like you can express it in terms of the Fourier transform of a Gaussian.

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