Class Bessel

java.lang.Object
cern.jet.math.Constants
cern.jet.math.Bessel
public class Bessel extends Constants
Bessel and Airy functions.

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    protected static final double[]
    A_i0
    Chebyshev coefficients for exp(-x) I0(x) in the interval [0,8].
    protected static final double[]
    A_i1
    Chebyshev coefficients for exp(-x) I1(x) / x in the interval [0,8].
    protected static final double[]
    A_k0
    COEFFICIENTS FOR METHODS k0, k0e *
    protected static final double[]
    A_k1
    COEFFICIENTS FOR METHODS k1, k1e *
    protected static final double[]
    B_i0
    Chebyshev coefficients for exp(-x) sqrt(x) I0(x) in the inverted interval [8,infinity].
    protected static final double[]
    B_i1
     
    protected static final double[]
    B_k0
     
    protected static final double[]
    B_k1
     

    Fields inherited from class Constants

    big, biginv, LOGPI, MACHEP, MAXGAM, MAXLOG, MINLOG, SQRTH, SQTPI

  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    protected
    Bessel()
    Makes this class non instantiable, but still let's others inherit from it.

  • Method Summary

    Modifier and Type
    Method
    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 Object

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

  • Field Details

    • A_i0

      protected static final double[] A_i0
      Chebyshev coefficients for exp(-x) I0(x) in the interval [0,8]. lim(x->0){ exp(-x) I0(x) } = 1.

    • B_i0

      protected static final double[] B_i0
      Chebyshev coefficients for exp(-x) sqrt(x) I0(x) in the inverted interval [8,infinity]. lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).

    • A_i1

      protected static final double[] A_i1
      Chebyshev coefficients for exp(-x) I1(x) / x in the interval [0,8]. lim(x->0){ exp(-x) I1(x) / x } = 1/2.

    • B_i1

      protected static final double[] B_i1

    • A_k0

      protected static final double[] A_k0
      COEFFICIENTS FOR METHODS k0, k0e *

    • B_k0

      protected static final double[] B_k0

    • A_k1

      protected static final double[] A_k1
      COEFFICIENTS FOR METHODS k1, k1e *

    • B_k1

      protected static final double[] B_k1

  • Constructor Details

    • Bessel

      protected Bessel()
      Makes this class non instantiable, but still let's others inherit from it.

  • Method Details

    • 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