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Thread: A nice integral

  1. May 20th 2008, 10:59 AM #1
    Veve
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    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.
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  2. May 20th 2008, 07:28 PM #2
    mr fantastic
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    Quote Originally Posted by Veve View Post
    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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