Bessel {Bessel} | R Documentation |
Compute the Bessel functions I(), J(), K(), and Y(), of complex
arguments z
and real nu
,
BesselI(z, nu, expon.scaled = FALSE, nSeq = 1) BesselJ(z, nu, expon.scaled = FALSE, nSeq = 1) BesselK(z, nu, expon.scaled = FALSE, nSeq = 1) BesselY(z, nu, expon.scaled = FALSE, nSeq = 1)
z |
complex or numeric vector. |
nu |
numeric (scalar). |
expon.scaled |
logical indicating if the result should be scaled by an exponential factor (typically to avoid under- or over-flow). |
nSeq |
positive integer; if > 1, computes the result for
a whole sequence of |
The case nu < 0
is handled by using simple formula from
Abramowitz and Stegun.
a complex or numeric vector (or matrix
with nSeq
columns if nSeq > 1
)
of the same length (or nrow
when nSeq > 1
) and
mode
as z
.
Donald E. Amos, Sandia National Laboratories, wrote the original fortran code. Martin Maechler did the R interface.
Abramowitz, M., and Stegun, I. A. (1955, etc). Handbook of mathematical functions (NBS AMS series 55, U.S. Dept. of Commerce).
D. E. Amos (1986) A portable package for Bessel functions of a complex argument and nonnegative order; ACM Trans. Math. Software 12, 3, 265–273.
D. E. Amos (1983) Computation of Bessel Functions of Complex Argument; Sand83-0083.
D. E. Amos (1983) Computation of Bessel Functions of Complex Argument and Large Order; Sand83-0643.
D. E. Amos (1985) A subroutine package for Bessel functions of a complex argument and nonnegative order; Sand85-1018.
Olver, F.W.J. (1974). Asymptotics and Special Functions; Academic Press, N.Y., p.420
The base R functions besselI
, etc.
## For real small arguments, BesselI() gives the same as base::besselI() : set.seed(47); x <- sort(round(rlnorm(20), 2)) M <- cbind(x, b = besselI(x, 3), B = BesselI(x, 3)) stopifnot(all.equal(M[,"b"], M[,"B"])) M