# Evaluating this contour integral

1. Feb 15, 2015

### Maybe_Memorie

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. Feb 20, 2015