Description Usage Arguments Details Value Author(s) References See Also Examples
Compute Bessel function I[nu](x)
and K[nu](x) for large x and small or moderate
nu, using the asymptotic expansion (9.7.1), p.377 of
Abramowitz & Stegun, for x -> Inf, even valid for
complex
x,
I_a(x) = exp(x) / sqrt(2*pi*x)* f(x, a),
where
f(x,a) = 1 - (mu-1) / (8x) + (mu-1)(mu-9) / (2! (8x)^2) - ...,
and mu = 4*a^2 and |arg(x)| < π/2.
Whereas besselIasym(x,a)
computes I_a(x),
besselI.ftrms
returns the corresponding terms in the
series expansion of f(x,a) above.
1 2 | besselIasym (x, nu, k.max = 10, expon.scaled = FALSE, log = FALSE)
besselI.ftrms(x, nu, K = 20)
|
x |
numeric, >= 0. |
nu |
numeric; The order (maybe fractional!) of the corresponding Bessel function. |
k.max, K |
integer number of terms in the expansion. |
expon.scaled |
logical; if |
log |
logical; if TRUE, \log(f(.)) is returned instead of f. |
......... FIXME ...
a numeric vector of the same length as x
.
Martin Maechler
Abramowitz, M., and Stegun, I. A. (1955, etc). Handbook of mathematical functions (NBS AMS series 55, U.S. Dept. of Commerce).
From this package Bessel() BesselI()
; further,
besselI.nuAsym()
which is useful when ν is large
(as well); further base besselI
, etc
1 2 3 4 5 6 7 |
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