std::legendre, std::legendref, std::legendrel

Computes the unassociated Legendre polynomials of the degree n and argument x.

# Declarations

double legendre( unsigned int n, double x );
double legendre( unsigned int n, float x );
double legendre( unsigned int n, long double x );
float legendref( unsigned int n, float x );
long double legendrel( unsigned int n, long double x );

double legendre( unsigned int n, IntegralType x );

# Parameters

n: the degree of the polynomial
x: the argument, a value of a floating-point or integral type

# Notes

Implementations that do not support TR 29124 but support TR 19768, provide this function in the header tr1/cmath and namespace std::tr1.

An implementation of this function is also available in boost.math.

The first few Legendre polynomials are:

# Example

#define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
#include <cmath>
#include <iostream>
 
double P3(double x)
{
    return 0.5 * (5 * std::pow(x, 3) - 3 * x);
}
 
double P4(double x)
{
    return 0.125 * (35 * std::pow(x, 4) - 30 * x * x + 3);
}
 
int main()
{
    // spot-checks
    std::cout << std::legendre(3, 0.25) << '=' << P3(0.25) << '\n'
              << std::legendre(4, 0.25) << '=' << P4(0.25) << '\n';
}