I am looking for a method of dealing with the modified Bessel function K_\nu(x) for large \nu.

The besselK function implementation of this allows for dealing with large values of x by allowing for exponential scaling, but there is no facility for dealing with large \nu.

What would work for me would be an lbesselK function in the manner of lgamma which returned the log of K_\nu(x) for large \nu. Does anybody have any leads on this?

Note that I have trawled through Abramowitz and Stegun and found 9.7.8 which doesn't work for me because of the complication in the definition of the x argument. I have also seen a result of Ismail (1977) reported by Barndorff-Nielsen and Blaesild which has the other problem, the treatment of the x argument is too simple.

To do the calculation I am attempting, I need to have the Bessel function in a form that will allow a cancellation with a Gamma function of high order in the denominator.

David Scott


--
_________________________________________________________________
David Scott     Department of Statistics
                The University of Auckland, PB 92019
                Auckland 1142,    NEW ZEALAND
Phone: +64 9 923 5055, or +64 9 373 7599 ext 85055
Email:  d.sc...@auckland.ac.nz,  Fax: +64 9 373 7018

Director of Consulting, Department of Statistics

______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Reply via email to