
Re: Removing singularity at x=0 for integral
Posted:
Nov 27, 2013 6:20 PM


On Tuesday, November 26, 2013 3:10:29 PM UTC5, Axel Vogt wrote: > On 26.11.2013 16:10, dspguy2t 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)
Hi Axel, Thanks for the help. Yes A>0. Given that I need to solve the integral numerically, integrating out to infinity becomes a little problematic (when A is very small). Most texts usually avoid the integration to infinity by making the reverse substitution.
I was able to make some progress by integrating by parts (see post below). The reason I'm integrating numerically is I'm also looking at a similar, but more difficult integral  which definitely can't be done in closed form.
Thanks, David

