## Bessel integral

Posted in R, Statistics, University life with tags , , , on September 28, 2011 by xi'an

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

$\int_a^\infty e^{-bt}\,I_n(t)\,\text{d}t\qquad a,b>0$

where In 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?