# A Is the pole in this integrand integrable?

Tags:
1. Apr 12, 2017

### junt

I am trying to numerically integrate the following complicated expression:

$$\frac{-2\exp{\frac{-4m(u^2+v^2+vw+w^2+u(v+w))}{\hbar^2\beta}-\frac{\hbar\beta(16\epsilon^2-8m\epsilon(-uv+uw+vw+w^2-4(u+w)\xi +8\xi^2)\omega^2+m^2(u^2+2v^2+2vw+w^2+2u(v+w-2\xi)-4w\xi+8\xi^2)(u^2+w^2-4(u+w)\xi+8\xi^2)\omega^4 )}{8m(u+w-4\xi)^2\omega^2}}}{|m(u+w-4\xi)\omega^2)|}$$

My integration variables are $u$, $v$ and $w$ from +$\infty$ to -$\infty$. Everything else are constants.

This is just an example of one integrand (motivated by a quantum mechanical system) where there exists infinitely many poles at $u+w=4\xi$. I am wondering if such poles are integrable. My pole is linear, and as a result quite simple. But I am really unable to prove if this pole is integrable or not. Does anybody have any idea about this problem? It would be a great help!

2. Apr 17, 2017

### scottdave

At first look, I would doubt it. Unless you could show some kind of symmetry, which would cancel out. Or you could show it is like the Del function, which is infinitely high, yet infintessimally small, so that the area under it is equal to 1. But this doesn't look like something which would do that.