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.