besselI(x, nu, expon.scaled=FALSE)
besselJ(x, nu, expon.scaled=FALSE)
besselK(x, nu, expon.scaled=FALSE)
besselY(x, nu, expon.scaled=FALSE)
TRUE
return
an exponential scale factor times the value of
the Bessel function, to remove the exponential
growth. Otherwise return the raw value of the Bessel function.
The scale factor depends on the Bessel function:
besselI:
exp(-abs(Re(x)))
,
besselJ:
exp(-abs(Im(x)))
,
besselK:
exp(x)
,
and besselY:
exp(-abs(Im(x)))
.
Note that this has no effect for besselJ and
besselY for real x.
The Bessel functions are computed using the double precision complex FORTRAN code written by D.E. Amos at Sandia National Laboratories. The code is available at www.netlib.org/amos.
The notation follows that of Abramowitz and Stegun, Handbook of Mathematical Functions.
besselJ(seq(0,3*pi,len=11), nu=0) # [1] 1.00000000 0.78996223 0.29056421 # [4] -0.19615024 -0.40198647 -0.26585725 # [7] 0.04517576 0.27371045 0.26075863 #[10] 0.04677168 -0.18121145