std::laguerre, std::laguerref, std::laguerrel
Min standard notice:
- 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
n: the degree of the polynomial, a value of unsigned integer typex: 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 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';
}