A nice integral

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May 20th 2008, 10:59 AM
Veve

A nice integral

I have a problem when it comes to calculate the next integral:

$\int_{-\infty}^\infty\frac{1}{(x+\tau)^k}e^{-2\pi ixn} dx$ where $n\in\mathbb{Z}, Im(\tau)>0.$

Any idea? Thanks.
May 20th 2008, 07:28 PM
mr fantastic

Quote:

Originally Posted by Veve

I have a problem when it comes to calculate the next integral:

$\int_{-\infty}^\infty\frac{1}{(x+\tau)^k}e^{-2\pi ixn} dx$ where $n\in\mathbb{Z}, Im(\tau)>0.$

Any idea? Thanks.

Look up (or calculate) the Fourier Transform of $\frac{1}{x^k}$ . Then apply (or prove and then apply) the shift theorem.

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