- #1
leialee
- 10
- 0
Homework Statement
How to integrate this?
##\int_{0}^{A} x e^{-a x^2}~ I_0(x) dx##
where ##I_0## is modified Bessel function of first kind?
I'm trying per partes and looking trough tables of integrals for 2 days now, and I would really really appreciate some help.
This is a part of a problem, whis would be this:
##T(r,z,t)=C\int_{0}^{B} u^{-\frac{3}{2}} du \int_{0}^{A} dr_0 r_0 e^{-\frac{r^2+r_0^2+z^2}{u}}~2\pi I_0(\frac{2rr_0}{u})####A=constant##
##B=4Dt##
##u=4D(t-t_0)##
and if the first integral isn't solvable with something relatively not- fancy as hmm let's say Marcum Q-function (cuz what even is that) how do i go about checking out limits for this second integral? Does anyone have any ideas?
1.) ##t\to \infty##
2.) ##r\to0##
3.) ##z=0##