Gaussian Integral with Denominator in QFT

["pi"mp]

Hi all, so I've come across the following Gaussian integral in QFT...but it has a denominator and I am completely stuck!

\int_{0}^{\infty} \frac{dx}{(x+i \epsilon)^{a}}e^{-B(x-A)^{2}}

where a is a power I need to leave arbitrary for now, but hope to take between 0 and 1, and \epsilon is arbitrarily small.

Does anyone have any suggestions on how to tackle this? If not, I'd like to leave a arbitrary, but perhaps is can be set to 1/2. Would this then be doable? Thanks for any help!

 

[RUber]

$\int_0^\infty \frac{e^{-B(x-A)^2}}{(x+i\epsilon)^a} \, dx$ could be rewritten as $\int_{i \epsilon} ^\infty \frac{e^{-B(z-A-i\epsilon)^2}}{(z)^a} \, dz$
I am thinking some sort of complex integration technique might help.