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Class jnt.functions.Bessel

java.lang.Object
   |
   +----jnt.functions.Bessel

public class Bessel
extends Object
Provides a collection of static functions for evaluating Bessel functions.

Example of use:
Print a table of the J0 Bessel function on [0,1].

int n = 20;
double x, left = 0.0, right = 1.0, dx = (right-left)/(double)n 
for (i=0, i<=n, i++) { x = left + (double)i*dx; System.out.println( x + " " + Bessel.J0(x) ); }

Version:
22 October 1997
Author:
Ronald F. Boisvert, NIST

Constructor Index

 o Bessel()

Method Index

 o I0(double)
Evaluates the hyperbolic Bessel function of the first kind of order 0 for a given real argument x.
 o I0e(double)
Evaluates the exponentially scalled hyperbolic Bessel function of the first kind of order 0 for a given real argument x.
 o I1(double)
Evaluates the hyperbolic Bessel function of the first kind of order 1 for a given real argument x.
 o I1e(double)
Evaluates the exponentially scalled hyperbolic Bessel function of the first kind of order 1 for a given real argument x.
 o J0(double)
Evaluates the Bessel function of the first kind of order 0 for a given real argument x.
 o J1(double)
Evaluates the Bessel function of the first kind of order 1 for a given real argument x.

Constructors

 o Bessel
 public Bessel()

Methods

 o J0
 public static double J0(double x) throws IllegalArgumentException
Evaluates the Bessel function of the first kind of order 0 for a given real argument x.

Note: This function throws IllegalArgumentException if |x| is so large that all precision in the result is lost.

Parameters:
x - (double)
The point at which the function is evaluated.
 o J1
 public static double J1(double x) throws IllegalArgumentException
Evaluates the Bessel function of the first kind of order 1 for a given real argument x.

Note: This function throws IllegalArgumentException if |x| is so large that all precision in the result is lost.

Parameters:
x - (double)
The point at which the function is evaluated.
 o I0
 public static double I0(double x) throws IllegalArgumentException
Evaluates the hyperbolic Bessel function of the first kind of order 0 for a given real argument x.

Note: This function throws IllegalArgumentException if |x| is so large that the result would overflow.

Parameters:
x - (double)
The point at which the function is evaluated.
 o I0e
 public static double I0e(double x)
Evaluates the exponentially scalled hyperbolic Bessel function of the first kind of order 0 for a given real argument x. The result computed is exp(-x)*I0(x). This function is useful in cases where I0(x) would overflow.

Parameters:
x - (double)
The point at which the function is evaluated.
 o I1
 public static double I1(double x) throws IllegalArgumentException
Evaluates the hyperbolic Bessel function of the first kind of order 1 for a given real argument x.

Note: This function throws IllegalArgumentException if |x| is so small that the result would underflow or if |x| is so large that the would overflow.

Parameters:
x - (double)
The point at which the function is evaluated.
 o I1e
 public static double I1e(double x)
Evaluates the exponentially scalled hyperbolic Bessel function of the first kind of order 1 for a given real argument x. The result computed is exp(-|x|)*I1(x). This function is useful in cases where I1(x) would overflow.

Parameters:
x - (double)
The point at which the function is evaluated.

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