**P**ierre Pudlo and I worked this morning on a distribution related to ~~philogenic~~ philogenetic trees and got stuck on the following Bessel integral

where ** I_{n}** is the modified Bessel function of the first kind. We could not find better than formula 6.611(4) in Gradshteyn and Ryzhik. which is for a=0… Anyone in for a closed form formula, even involving special functions?