Date: Nov 26, 2013 10:10 AM
Subject: Removing singularity at x=0 for integral
Hi I'm trying to numerically integrate the following expression from 0 .. 1
f(x)=1/x^1.5 * exp(-A/x) , where A is a constant.
As x->0, the exponential goes to zero faster than the power, so f(x)->0, as x-> 0.
I'm evaluating this integral at various values of A - there are cases when A is very small.
I'm trying to find a way to remove the singularity at x=0. I've looked at the usual techniques, like integration by parts, subtracting the singularity out, change of variables.
The change of variables is usually done when the power is less than one e.g.(1/sqrt(x)). exp(-A/x) is not analytic so integration by parts seems problematic.
Thanks for any assistance.