# A nice integral

• May 20th 2008, 11:59 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, 08:28 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.