# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.analysis.integration.univariate.riemann.gaussian.rule

## Class LegendrePolynomials

• java.lang.Object
• com.numericalmethod.suanshu.analysis.integration.univariate.riemann.gaussian.rule.LegendrePolynomials
• All Implemented Interfaces:
OrthogonalPolynomialFamily

public class LegendrePolynomials
extends Object
implements OrthogonalPolynomialFamily
A Legendre polynomial is defined by the recurrence relation below. $P_0(x) = 1,\quad P_1(x) = x, \quad (n+1) P_{n+1}(x) = (2n+1) x P_n(x) - n P_{n-1}(x).$

Legendre polynomials are derived from a differential equation encountered in physics and engineering.