com.hedgehog.math.functions
Class LogarithmicIntegralFunction

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

All Implemented Interfaces:

java.lang.Comparable, java.util.Comparator

public class LogarithmicIntegralFunction
extends Function

Title: LogarithmicIntegralFunction - represents the logarithmic integral function li(x).

Description: Represents the logarithmic integral function li(x), which is sometimes referred to as the "American" definition.

The function is evaluated using the Nielsen-Ramanujan formula.

Some special case values are:

 li(0.0)      : 0.0
 li(1.0)      : -1.0E20
 li(2.0)      : 1.045163768060353
 li(1.451...) : 0.0
 

For further details refer to MathWorld.

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

Company: Hedgehog Software

Since:

1.0

Version:

1.1

Field Summary

protected double

mTolerance Tolerance used for convergence.

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

method

Fields inherited from class com.hedgehog.HObject

mID, mName

Constructor Summary

LogarithmicIntegralFunction(double tolerance)
Constructor.

LogarithmicIntegralFunction(LogarithmicIntegralFunction object)
Copy constructor.

Method Summary

double	getValue(double x) Evaluates li(x).
boolean	isValid() Tests whether or not a valid object.
double	Li(double x) Evaluates Li(x)=li(x)-li(2), which is sometimes referred to as the "European" definition.

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

Field Detail

mTolerance

protected double mTolerance

Tolerance used for convergence.

Constructor Detail

LogarithmicIntegralFunction

public LogarithmicIntegralFunction(double tolerance)

Constructor.

Parameters:

tolerance - Required tolerance of accuracy of evaluation of li(x).

LogarithmicIntegralFunction

public LogarithmicIntegralFunction(LogarithmicIntegralFunction object)

Copy constructor.

Parameters:

object - Object to copy.

Method Detail

getValue

public double getValue(double x)

Evaluates li(x). Note that li(1.0) is equal to -infinity and this method returns com.hedgehog.utility.Tolerances.NEGATIVE_INFINITE.

Parameters:

x - Value at which li(x) is to evaluated.

Returns:

Evaluation of li(x).

Li

public double Li(double x)

Evaluates Li(x)=li(x)-li(2), which is sometimes referred to as the "European" definition. The value of Li(x) as x becomes large provides an estimate for pi(x), where pi(x) is the prime counting function; see MathWorld.

Parameters:

x - Value at which to evaluate Li(x).

Returns:

Evaluation of Li(x).

isValid

public boolean isValid()

Tests whether or not a valid object.

Specified by:

isValid in class Function

Returns:

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