I have the following double integral: $\int\limits_0^x {\int\limits_0^y {{e^{  {K_1}(u + v)}}{I_0}\left( {2{K_1}\sqrt {uv} } \right)dudv} }$ where $K_1$ is a constant. Do you have any ideas of getting a closed form for this integral? Thank you very much.

To Jochen Wengenroth, my guess is I_{0} is a modified Bessel function. To the OP. I have no expertise when it comes to this, but if it is a Bessel function, converting it to some polar form of some kind might help. 


I found the solution from a reference paper, which is: A Double Integral Containing the Modified Bessel Function: Asymptotics and Computation. http://www.ams.org/journals/mcom/198647176/S0025571819860856712X/S0025571819860856712X.pdf 

