Bessel_mpfr {Rmpfr} | R Documentation |
Bessel functions of integer orders, provided via arbitrary precision algorithms from the MPFR library.
Note that the computation can be very slow when n
and
x
are large (and of similar magnitude).
Ai(x) j0(x) j1(x) jn(n, x, rnd.mode = c("N","D","U","Z","A")) y0(x) y1(x) yn(n, x, rnd.mode = c("N","D","U","Z","A"))
x |
|
n |
non-negative integer (vector). |
rnd.mode |
a 1-letter string specifying how rounding
should happen at C-level conversion to MPFR, see |
Computes multiple precision versions of the Bessel functions of integer order, J[n](x) and Y[n](x), and—when using MPFR library 3.0.0 or newer—also of the Airy function Ai(x).
besselJ
, and besselY
compute the
same bessel functions but for arbitrary real order and only
precision of a bit more than ten digits.
x <- (0:100)/8 # (have exact binary representation) stopifnot( all.equal(besselY(x, 0), bY0 <- y0(x)) , all.equal(besselJ(x, 1), bJ1 <- j1(x)) , all.equal(yn(0,x), bY0) , all.equal(jn(1,x), bJ1) )