Package org.opensourcephysics.numerics.specialfunctions

Class Chebyshev

java.lang.Object

org.opensourcephysics.numerics.specialfunctions.Chebyshev

public class Chebyshev
extends java.lang.Object

Chebyshev defines Chebyshev polynomials Tn(x) and Un(x) using the well known recurrence relationships. The information needed for this class was gained from Alan Jeffrey's Handbook of Mathematical Formulas and Integrals, 3rd Edition pages 290-295. Chebyshev polynomials are used to solve differential equations of second order, hence why we have two different types. This code is based on the Open Source Physics class for Hermite polynomials.

Method Summary

Modifier and Type	Method	Description
static Polynomial	getPolynomialT(int n)	This method returns the nth polynomial of type T.
static Polynomial	getPolynomialU(int n)	This method returns the nth polynomial of type U.

Methods inherited from class java.lang.Object

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

Method Detail

getPolynomialT

public static Polynomial getPolynomialT(int n)

This method returns the nth polynomial of type T. If it has already been calculated it just returns it from the list. If we have not calculated it uses the recursion relationship to calculate based off of the prior polynomials.

getPolynomialU

public static Polynomial getPolynomialU(int n)

This method returns the nth polynomial of type U. If it has already been calculated it just returns it from the list. If we have not calculated it uses the recursion relationship to calculate based off of the prior polynomials.