Rmpfr (version 0.5-3)

Bessel_mpfr: Bessel functions of Integer Order in multiple precisions

Description

Bessel functions of integer orders, provided via arbitrary precision algorithms from the MPFR library.

Usage

Ai(x)
j0(x)
j1(x)
jn(n, x)
y0(x)
y1(x)
yn(n, x)

Arguments

x

a numeric or mpfr vector.

n

non-negative integer (vector).

Value

• 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 $Ai(x)$.

See Also

besselJ, and besselY compute the same bessel functions but for arbitrary real order and only precision of a bit more than ten digits.

Examples

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)
         )

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