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Evaluating this contour integral

  1. Feb 15, 2015 #1
    I was reading a paper which featured the following horrendous integral
    ##\displaystyle\prod_{n=1}^L\oint_{C_n}\frac{dx_n}{2\pi i}\prod_{k<l}^L(x_k-x_l)\prod_{m=1}^L\frac{Q_w(x_m)}{Q^+_\theta(x_m)Q^-_\theta(x_m)}##

    where ##Q^\pm_\theta(x)=\prod_{k=1}^L(u-\theta_k\pm \frac{i}{2})## and ##Q_w(x)=\prod_{r=1}^M(x-w_r)##.

    From the paper, ##C_n## denotes the integration contour which encloses ##\theta_n \pm \frac{i}{2}## counterclockwise.

    Obviously I can just use the residue theorem and sum over the poles to evaluate it but I'm having trouble doing that since the thing is so complicated. How do I write this as a residue? Can I just focus on the denominators and ignore the other parts?
     
  2. jcsd
  3. Feb 20, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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