# Bessel_mpfr: Bessel functions of Integer Order in multiple precisions In Rmpfr: R MPFR - Multiple Precision Floating-Point Reliable

## Description

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).

## Usage

 ```1 2 3 4 5 6 7``` ```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")) ```

## Arguments

 `x` a `numeric` or `mpfr` vector. `n` non-negative integer (vector). `rnd.mode` a 1-letter string specifying how rounding should happen at C-level conversion to MPFR, see `mpfr`.

## 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

 ```1 2 3 4 5 6``` ```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) ) ```

Rmpfr documentation built on May 29, 2017, 2:19 p.m.