[R] Bessel function with large index value

[David Scott]

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.scott at auckland.ac.nz,  Fax: +64 9 373 7018

Director of Consulting, Department of Statistics