Bessel integral

September 28, 2011
By

(This article was first published on Xi'an's Og » R, and kindly contributed to R-bloggers)

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

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?


Filed under: R, Statistics, University life Tagged: ABC, Bessel functions, philogenic trees

To leave a comment for the author, please follow the link and comment on his blog: Xi'an's Og » R.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...



If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Tags: , , , , ,

Comments are closed.