Is there any general solution of contour integral with higher order poles on real axis?
I have got one but valid for simple pole only.
$\mathbf{P}\int\limits_{-\infty}^{\infty}Q(x)\mathrm{d}x=2\pi\mathrm{i}\sum\limits_{y>0}\mathrm{Res}[Q(z)]+\pi\mathrm{i}\sum\limits_{y=0}\mathrm{Res}[Q(z)]$
I have the integral with form like this:- $\int\limits_{-\infty}^{\infty}\frac{(Az^2+\mathrm{i}Bz+C)\mathrm{e}^{-\mathrm{i}za}}{z^2(A_0z^2+\mathrm{i}Bz+C)}\mathrm{d}z\quad$ where, $\quad a,A,A_0,B,C>0$