- #1
"pi"mp
- 129
- 1
Hi all, so I've come across the following Gaussian integral in QFT...but it has a denominator and I am completely stuck!
[tex] \int_{0}^{\infty} \frac{dx}{(x+i \epsilon)^{a}}e^{-B(x-A)^{2}} [/tex]
where a is a power I need to leave arbitrary for now, but hope to take between 0 and 1, and [itex] \epsilon [/itex] 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!
[tex] \int_{0}^{\infty} \frac{dx}{(x+i \epsilon)^{a}}e^{-B(x-A)^{2}} [/tex]
where a is a power I need to leave arbitrary for now, but hope to take between 0 and 1, and [itex] \epsilon [/itex] 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!