R: Calculation of the Incomplete BesselK Functions in Terms of...
besselK_inc_err
R Documentation
Calculation of the Incomplete BesselK Functions in Terms of the Complementary Error Functions
Description
Calculates incomplete BesselK functions by evaluating explicit
expressions for the lower and upper incomplete BesselK in terms
of the complementary error function by calling CalIncLapInt.
Barndorff-Nielsen, O. E (1977) Exponentially decreasing
distributions for the logarithm of particle size. Proceedings
of the Royal Society of London. Series A, 353, 401–419.
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.
Tran, T. T., Yee, W.T. and Tee, J.G (2012) Formulae for the Extended
Laplace Integral and Their Statistical Applications. Working Paper.
Watson, G.N (1931) A Treatise on the Theory of Bessel
Functions and Their Applications to Physics. London: MacMillan and Co.
See Also
besselK_inc_clo, gamma_inc_clo, pgig
Examples
## Accuracy tests
x <- 2
z <- 5
lambda <- -c(1/2, 3/2)
lower <- sapply(lambda, function(w.)
besselK_inc_err(x, z, lambda = w., 200, lower = TRUE))
upper <- sapply(lambda, function(w.)
besselK_inc_err(x, z, lambda = w., 200, lower = FALSE))
## sum of two parts
(lower + upper)
## equals the whole function
(besselK(z, nu = lambda))