1. Sep 21, 2012 #1

   kbrijesh

   

   how to get the fourier transform of (1+at^2)^-n ? n is a natural number such that (n>1) and a is any positive number.
   
   i.e. ∫((1+at^2)^-n)*exp(-jωt)dt; limits of integration goes from -∞ to ∞

    

   kbrijesh, Sep 21, 2012
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3. Sep 21, 2012 #2

   jackmell

   

   You can do it via contour integration for specific small n but not sure for general n. But first, look at a simple case:
   
   [tex]\int_{-\infty}^{\infty} \frac{e^{-i\omega t}}{(1+2t^2)^2}dt[/tex]
   
   Now that can be solved by the Residue Theorem. First get that one straight, then go on to n=3, maybe 4, then try and come up with an expression for the general case.

    

   jackmell, Sep 21, 2012
4. Sep 24, 2012 #3

   kbrijesh

   

   
   
   Yes, you are true. Even using contour integration we can do it upto n=3. But I am y\trying to get a generalized solution.
   
   Anyway, thanks for your reply.

    

   kbrijesh, Sep 24, 2012

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