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Homework Help: Residue theorem appliation

  1. Mar 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Calculate the integral [tex] I(k)= \int_{-\infty}^{\infty} \frac{dx}{(x^{2}+1)^{k}} [/tex] with 'k' being a real number



    2. Relevant equations the integral equation above




    3. The attempt at a solution

    from the residue theorem , there is a pole of order one at [tex] 2+ix=0 [/tex] , my problem is the pole of order 'k' at s=i and s=-i , in order to handel with this pole i have thought that using residue theorem

    [tex] \frac{1}{\Gamma(s)}D^{k-1}((s-i)^{k}\frac{1}{(x^{2}+1)^{k}} [/tex]

    evaluated at both s=i and s=-i
     
  2. jcsd
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