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Topic: Removing singularity at x=0 for integral
Replies: 7   Last Post: Nov 28, 2013 3:25 PM

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Robin Vowels

Posts: 30
Registered: 12/17/11
Re: Removing singularity at x=0 for integral
Posted: Nov 26, 2013 10:10 PM
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On Wednesday, November 27, 2013 2:10:25 AM UTC+11, dsp...@netscape.net wrote:
> 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. Any suggestions? Thanks for any assistance.

It doesn't matter whether the exponentail goes to zero faster than the power.
The fact is that you can't divide by zero in both the exponential and the power.

You could try taking logs, but you still can't evaluate at x = 0;
however you can get close to it.




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