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
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