std::laguerre, std::laguerref, std::laguerrel

  1. Computes the non-associated Laguerre polynomials of the degree n and argument x.

# Declarations

double laguerre( unsigned int n, double x );
double laguerre( unsigned int n, float x );
double laguerre( unsigned int n, long double x );
float laguerref( unsigned int n, float x );
long double laguerrel( unsigned int n, long double x );
double laguerre( unsigned int n, IntegralType x );

# Parameters

# 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 Laguerre polynomials are the polynomial solutions of the equation xy,, + (1 - x)y, + ny = 0.

The first few are:

# Example

#define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
#include <cmath>
#include <iostream>
 
double L1(double x)
{
    return -x + 1;
}
 
double L2(double x)
{
    return 0.5 * (x * x - 4 * x + 2);
}
 
int main()
{
    // spot-checks
    std::cout << std::laguerre(1, 0.5) << '=' << L1(0.5) << '\n'
              << std::laguerre(2, 0.5) << '=' << L2(0.5) << '\n';
}

# See also