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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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Axel Vogt

Posts: 1,038
Registered: 5/5/07
Re: Removing singularity at x=0 for integral
Posted: Nov 26, 2013 3:10 PM
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On 26.11.2013 16:10, dspguy2@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.
> David


Guessing you mean 0 < A the value is -Pi^(1/2)*(erf(A^(1/2))-1)/A^(1/2) by Maple

Note that you do not need 'analytic', so x = 1/t^2 is allowed here and will
give what Maple says for Int(2*exp(-A*t^2), t = 1 .. infinity)





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