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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.

flag	asked Jan 10 at 8:14 Binh Nguyen 1●2

What is the function $I_0$? You can get rid of the constant by substitution. – Jochen Wengenroth Jan 10 at 9:36

Taiyo Terada · Answer 1 · 2013-01-10 10:15:44Z UTC

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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.

answered Jan 10 at 10:15

Taiyo Terada
11●1

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I found the solution from a reference paper, which is: A Double Integral Containing the Modified Bessel Function: Asymptotics and Computation. – Binh Nguyen Jan 23 at 11:34

For anyone interested, here's a link to the paper unknown (google) cited: ams.org/journals/mcom/1986-47-176/… – Barry Cipra Jan 24 at 19:28

@Binh Nguyen: Please, post this as an answer and accept it, so that the software does not bump the question periodically thinking it is unanswered. – Emil Jeřábek Feb 7 at 11:39

Binh Nguyen · Accepted Answer · 2013-04-12 12:39:59Z UTC

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/1986-47-176/S0025-5718-1986-0856712-X/S0025-5718-1986-0856712-X.pdf

Closed form for double integral?

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