std::hermite, std::hermitef, std::hermitel

  1. 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

# 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';
}

# See also