std::hermite, std::hermitef, std::hermitel
Min standard notice:
- Computes the (physicist’s) Hermite polynomials of the degree n and argument x.
# Declarations
double hermite( unsigned int n, double x );
double hermite( unsigned int n, float x );
double hermite( unsigned int n, long double x );
float hermitef( unsigned int n, float x );
long double hermitel( unsigned int n, long double x );
double hermite( unsigned int n, IntegralType x );
# Parameters
n: the degree of the polynomialx: 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 Hermite polynomials are the polynomial solutions of the equation u,, - 2xu, = -2nu.
The first few are:
# Example
#define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
#include <cmath>
#include <iostream>
double H3(double x)
{
return 8 * std::pow(x, 3) - 12 * x;
}
double H4(double x)
{
return 16 * std::pow(x, 4) - 48 * x * x + 12;
}
int main()
{
// spot-checks
std::cout << std::hermite(3, 10) << '=' << H3(10) << '\n'
<< std::hermite(4, 10) << '=' << H4(10) << '\n';
}