com.hedgehog.math.functions
Class BesselFunction

java.lang.Object
  com.hedgehog.HObject
      com.hedgehog.math.functions.Function
          com.hedgehog.math.functions.BesselFunction

All Implemented Interfaces:

java.lang.Comparable, java.util.Comparator

public final class BesselFunction
extends Function

Title: BesselFunction - represents Bessel functions.

Description: Provides static Bessel functions.

Bessel's second order differential equation occurs repeatedly in astronomy, heat conduction, electricity, stress in beams, etc. The general equation of order no is x^2y'' + xy' + (x^2-n^2) = 0.

For detailed information regarding Bessel functions refer to any good mathematics book, such as Chapter 6 of Peter O'Neil's "Advanced Engineering Mathematics", Wadsworth Pub., 1983.

Copyright: Copyright (c) Hedgehog Software 2007-2009.

Company: Hedgehog Software.

Since:

1.0

Version:

1.1

Field Summary

Fields inherited from class com.hedgehog.math.functions.Function

method

Fields inherited from class com.hedgehog.HObject

mID, mName

Constructor Summary

BesselFunction()
Default constructor.

BesselFunction(BesselFunction object)
Copy constructor.

Method Summary

boolean	isValid() Tests whether or not a valid object.
static double	j0(double x) Evaluates J0(x).
OneVariablePolynomial	j0Polynomial(int nTerms) Returns J0(x) as a polynomial object.
double[]	j0Roots(int numberOfRoots) Returns the roots of J0(x)=0 upto and including the specified number of roots, which cannot exceed 30.
static double	j1(double x) Evaluates J1(x).
static double	jn(int n, double x) Evaluates Jn(x).
OneVariablePolynomial	jnPolynomial(int n, int nTerms) Returns Jn(x) as a polynomial object.
static double	y0(double x) Evaluates Y0(x).
static double	y1(double x) Evaluates Y1(x).
static double	yn(int n, double x) Evaluates Yn(x).

Methods inherited from class com.hedgehog.math.functions.Function

getMethod, setMethod, toString

Methods inherited from class com.hedgehog.HObject

clone, compare, compareTo, copy, equals, getID, getName, hashCode, hasID, hasName, setID, setName

Methods inherited from class java.lang.Object

finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

BesselFunction

public BesselFunction()

Default constructor.

BesselFunction

public BesselFunction(BesselFunction object)

Copy constructor.

Parameters:

object - Object to copy.

Method Detail

j0

public static double j0(double x)

Evaluates J0(x).

Parameters:

x - Value of x.

Returns:

The Bessel function of the first kind of order 0 of the argument; J0(x).

j1

public static double j1(double x)

Evaluates J1(x).

Parameters:

x - Value of x.

Returns:

The Bessel function of the first kind of order 1 of the argument; J1(x).

jn

public static double jn(int n,
                        double x)

Evaluates Jn(x).

Parameters:

n - Order.

x - Value of x.

Returns:

The Bessel function of the first kind of order n of the argument; Jn(x).

y0

public static double y0(double x)

Evaluates Y0(x).

Parameters:

x - Value of x.

Returns:

Value of Y0(x).

y1

public static double y1(double x)

Evaluates Y1(x).

Parameters:

x - Value of x.

Returns:

Value of Y1(x).

yn

public static double yn(int n,
                        double x)

Evaluates Yn(x).

Parameters:

n - Order.

x - Value of x.

Returns:

Value of Yn(x).

jnPolynomial

public OneVariablePolynomial jnPolynomial(int n,
                                          int nTerms)
                                   throws java.lang.IllegalArgumentException

Returns Jn(x) as a polynomial object.

Parameters:

n - Order of Jn(x).

nTerms - Number of terms in polynomial.

Returns:

Jn(x) as polynomial.

Throws:

java.lang.IllegalArgumentException - Thrown if n < 0 or nTerms <= 0.

j0Polynomial

public OneVariablePolynomial j0Polynomial(int nTerms)
                                   throws java.lang.IllegalArgumentException

Returns J0(x) as a polynomial object.

Parameters:

nTerms - Number of terms in polynomial.

Returns:

J0(x) as polynomial.

Throws:

java.lang.IllegalArgumentException - Thrown if nTerms <= 0.

j0Roots

public double[] j0Roots(int numberOfRoots)
                 throws java.lang.IllegalArgumentException

Returns the roots of J0(x)=0 upto and including the specified number of roots, which cannot exceed 30. The positive roots of J0(x)=0 are frequently required when dealing with Bessel functions.

Parameters:

numberOfRoots - The number of roots in range [1:30].

Returns:

1D Java array of roots.

Throws:

java.lang.IllegalArgumentException - Thrown if numberOfRoots outside range [1:30].

isValid

public boolean isValid()

Description copied from class: Function

Tests whether or not a valid object.

Specified by:

isValid in class Function

Returns:

Logical-true if a valid object, else logical-false.