std::assoc_laguerre, std::assoc_laguerref, std::assoc_laguerrel
Min standard notice:
- Computes the associated Laguerre polynomials of the degree n, order m, and argument x.
# Declarations
double assoc_laguerre ( unsigned int n, unsigned int m, double x );
double assoc_laguerre ( unsigned int n, unsigned int m, float x );
double assoc_laguerre ( unsigned int n, unsigned int m, long double x );
float assoc_laguerref( unsigned int n, unsigned int m, float x );
long double assoc_laguerrel( unsigned int n, unsigned int m, long double x );
double assoc_laguerre ( unsigned int n, unsigned int m, IntegralType x );
# Parameters
n: the degree of the polynomial, a value of unsigned integer typem: the order 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 associated Laguerre polynomials are the polynomial solutions of the equation xy,, + (m + 1 - x)y, + ny = 0.
The first few are:
# Example
#define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
#include <cmath>
#include <iostream>
double L1(unsigned m, double x)
{
return -x + m + 1;
}
double L2(unsigned m, double x)
{
return 0.5 * (x * x - 2 * (m + 2) * x + (m + 1) * (m + 2));
}
int main()
{
// spot-checks
std::cout << std::assoc_laguerre(1, 10, 0.5) << '=' << L1(10, 0.5) << '\n'
<< std::assoc_laguerre(2, 10, 0.5) << '=' << L2(10, 0.5) << '\n';
}