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
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
References
Abramowitz, M. and Stegun, I. A. 1972. Chapter 9: Bessel Functions of Integer Order. Handbook of Mathematical Functions. New York, NY: Dover.
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)