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cern.jet.math
Class Bessel

java.lang.Object
  extended bycern.jet.math.Constants
      extended bycern.jet.math.Bessel
public class Bessel
extends Constants

Bessel and Airy functions.

Method Summary
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 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:
ArithmeticException

i0e

public static double i0e(double x)
                  throws 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:
ArithmeticException

i1

public static double i1(double x)
                 throws 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:
ArithmeticException

i1e

public static double i1e(double x)
                  throws 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:
ArithmeticException

j0

public static double j0(double x)
                 throws 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:
ArithmeticException

j1

public static double j1(double x)
                 throws 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:
ArithmeticException

jn

public static double jn(int n,
                        double x)
                 throws 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:
ArithmeticException

k0

public static double k0(double x)
                 throws 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:
ArithmeticException

k0e

public static double k0e(double x)
                  throws 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:
ArithmeticException

k1

public static double k1(double x)
                 throws 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:
ArithmeticException

k1e

public static double k1e(double x)
                  throws 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:
ArithmeticException

kn

public static double kn(int nn,
                        double x)
                 throws 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:
ArithmeticException

y0

public static double y0(double x)
                 throws 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:
ArithmeticException

y1

public static double y1(double x)
                 throws 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:
ArithmeticException

yn

public static double yn(int n,
                        double x)
                 throws 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:
ArithmeticException
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