cern.jet.math.tdouble

Class Bessel

java.lang.Object

cern.jet.math.tdouble.DoubleConstants

cern.jet.math.tdouble.Bessel

public class Bessel
extends DoubleConstants

Bessel and Airy functions.

Method Summary

Modifier and Type	Method and Description
static double	i0(double x) Returns the modified Bessel function of order 0 of the argument.
static double	i0e(double x) Returns the exponentially scaled modified Bessel function of order 0 of the argument.
static double	i1(double x) Returns the modified Bessel function of order 1 of the argument.
static double	i1e(double x) Returns the exponentially scaled modified Bessel function of order 1 of the argument.
static double	j0(double x) Returns the Bessel function of the first kind of order 0 of the argument.
static double	j1(double x) Returns the Bessel function of the first kind of order 1 of the argument.
static double	jn(int n, double x) Returns the Bessel function of the first kind of order n of the argument.
static double	k0(double x) Returns the modified Bessel function of the third kind of order 0 of the argument.
static double	k0e(double x) Returns the exponentially scaled modified Bessel function of the third kind of order 0 of the argument.
static double	k1(double x) Returns the modified Bessel function of the third kind of order 1 of the argument.
static double	k1e(double x) Returns the exponentially scaled modified Bessel function of the third kind of order 1 of the argument.
static double	kn(int nn, double x) Returns the modified Bessel function of the third kind of order nn of the argument.
static double	y0(double x) Returns the Bessel function of the second kind of order 0 of the argument.
static double	y1(double x) Returns the Bessel function of the second kind of order 1 of the argument.
static double	yn(int n, double x) Returns the Bessel function of the second kind of order n of the argument.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

i0

public static double i0(double x)
                 throws java.lang.ArithmeticException

Returns the modified Bessel function of order 0 of the argument.

The function is defined as i0(x) = j0( ix ).

The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

Parameters:

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

i0e

public static double i0e(double x)
                  throws java.lang.ArithmeticException

Returns the exponentially scaled modified Bessel function of order 0 of the argument.

The function is defined as i0e(x) = exp(-|x|) j0( ix ).

Parameters:

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

i1

public static double i1(double x)
                 throws java.lang.ArithmeticException

Returns the modified Bessel function of order 1 of the argument.

The function is defined as i1(x) = -i j1( ix ).

The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

Parameters:

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

i1e

public static double i1e(double x)
                  throws java.lang.ArithmeticException

Returns the exponentially scaled modified Bessel function of order 1 of the argument.

The function is defined as i1(x) = -i exp(-|x|) j1( ix ).

Parameters:

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

j0

public static double j0(double x)
                 throws java.lang.ArithmeticException

Returns the Bessel function of the first kind of order 0 of the argument.

Parameters:

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

j1

public static double j1(double x)
                 throws java.lang.ArithmeticException

Returns the Bessel function of the first kind of order 1 of the argument.

Parameters:

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

jn

public static double jn(int n,
                        double x)
                 throws java.lang.ArithmeticException

Returns the Bessel function of the first kind of order n of the argument.

Parameters:

n - the order of the Bessel function.

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

k0

public static double k0(double x)
                 throws java.lang.ArithmeticException

Returns the modified Bessel function of the third kind of order 0 of the argument.

The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

Parameters:

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

k0e

public static double k0e(double x)
                  throws java.lang.ArithmeticException

Returns the exponentially scaled modified Bessel function of the third kind of order 0 of the argument.

Parameters:

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

k1

public static double k1(double x)
                 throws java.lang.ArithmeticException

Returns the modified Bessel function of the third kind of order 1 of the argument.

The range is partitioned into the two intervals [0,2] and (2, infinity). Chebyshev polynomial expansions are employed in each interval.

Parameters:

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

k1e

public static double k1e(double x)
                  throws java.lang.ArithmeticException

Returns the exponentially scaled modified Bessel function of the third kind of order 1 of the argument.

k1e(x) = exp(x) * k1(x).

Parameters:

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

kn

public static double kn(int nn,
                        double x)
                 throws java.lang.ArithmeticException

Returns the modified Bessel function of the third kind of order nn of the argument.

The range is partitioned into the two intervals [0,9.55] and (9.55, infinity). An ascending power series is used in the low range, and an asymptotic expansion in the high range.

Parameters:

nn - the order of the Bessel function.

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

y0

public static double y0(double x)
                 throws java.lang.ArithmeticException

Returns the Bessel function of the second kind of order 0 of the argument.

Parameters:

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

y1

public static double y1(double x)
                 throws java.lang.ArithmeticException

Returns the Bessel function of the second kind of order 1 of the argument.

Parameters:

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException

yn

public static double yn(int n,
                        double x)
                 throws java.lang.ArithmeticException

Returns the Bessel function of the second kind of order n of the argument.

Parameters:

n - the order of the Bessel function.

x - the value to compute the bessel function of.

Throws:

java.lang.ArithmeticException