Bessel
Bessel functions

### Description

Bessel functions of the first and second kind (J, Y) and modified Bessel functions of the first and second kind (I, K) for real nonnegative x and real order (nu).

### Usage

    besselJ(x, nu)
    besselY(x, nu)
    besselI(x, nu, expon.scaled = FALSE)
    besselK(x, nu, expon.scaled = FALSE)

### Arguments

x | A numeric vector of nonnegative values.
nu | A numeric vector giving the order of the Bessel function.
expon.scaled | A logical value. If 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(-x), besselK: exp(x).

### Details

The Bessel functions are computed using Boost: (http://www.boost.org/doc/libs/1_47_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel.html)
Value

besselJ, besselY | return the value of the Bessel function of the first and second kind respectively.
besselI, besselK | return the value of the modified Bessel function of the first and second kind respectively.

Differences between Spotfire Enterprise Runtime for R and Open-source R
The Bessel functions are computed using Boost (http://www.boost.org/doc/libs/1_47_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel.html).
References
Abramowitz, M. and Stegun, I. A. 1972. Chapter 9: Bessel Functions of Integer Order. Handbook of Mathematical Functions. New York, NY: Dover.
http://en.wikipedia.org/wiki/Bessel_function.
Examples

    x <- seq(0, 4, length.out = 20)
    besselJ(x, 1:4)
    besselY(x, -1:4)
    besselI(x, 10, expon.scaled = TRUE)
    besselK(x, 20, expon.scaled = TRUE)

Package base version 6.1.5-18
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