besselK_inc_clo evaluates
closed-form formulae, which we derived to compute this
integral, in the (0, x) and (x, ∞) intervals
for the so-called lower and upper incomplete Bessel
function respectively. “Exact" evaluation of the integral
in these intervals can also be obtained by
numerical integration using software such
as Maple www.maple.com.
Olver, F.W.J., Lozier, D.W., Boisver, R.F. and Clark,
C.W (2010) Handbook of Mathematical Functions.
New York: National Institute of Standards and Technology,
and Cambridge University Press.
Watson, G.N (1931) A Treatise on the Theory of
Bessel Functions and Their Applications to Physics.
London: MacMillan and Co.
See Also
besselK_app_ser, besselK_inc_erfc
Examples
options(digits = 15)
## For x = 5, z = 8, lambda = 15/2 Maple 15 gives exact value of the
## lower incomplete Bessel function 0.997 761 151 460 5189(-4)
besselK_inc_clo(5, 8, 15/2, lower = TRUE, expon.scaled = FALSE)
## For x = 21, z = 8, lambda = 21/2 Maple 15 give exact value of the
## upper incomplete Bessel function 0.704 812 324 921 884 3938(-2)
besselK_inc_clo(21, 8, 21/2, lower = FALSE, expon.scaled = FALSE)