Bessel integral

Posted on September 28, 2011 by xi'an in R bloggers | 0 Comments

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

$\int_a^\infty e^{-bt}\,I_n(t)\,\text{d}t\qquad a,b>0$ 0′ title=’\int_a^\infty e^{-bt}\,I_n(t)\,\text{d}t\qquad a,b>0′ class=’latex’ />

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?