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

Since C++23

Header: <cmath>

1-3) Computes the (physicist’s) Hermite polynomials of the degree n and argument x.The library provides overloads of std::hermite for all cv-unqualified floating-point types as the type of the parameter x.(since C++23)

# Declarations

double hermite ( unsigned int n, double x );
float hermite ( unsigned int n, float x );
long double hermite ( unsigned int n, long double x );

(since C++17) (until C++23)

/* floating-point-type */ hermite( unsigned int n,
/* floating-point-type */ x );

(since C++23)

float hermitef( unsigned int n, float x );

(since C++17)

long double hermitel( unsigned int n, long double x );

(since C++17)

Additional overloads

template< class Integer >
double hermite ( unsigned int n, Integer x );

(since C++17)

# Parameters

# Notes

Implementations that do not support C++17, but support ISO 29124:2010, provide this function if STDCPP_MATH_SPEC_FUNCS is defined by the implementation to a value at least 201003L and if the user defines STDCPP_WANT_MATH_SPEC_FUNCS before including any standard library headers.

Implementations that do not support ISO 29124:2010 but support TR 19768:2007 (TR1), 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:

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::hermite(int_num, num) has the same effect as std::hermite(int_num, static_cast(num)).

# Example

#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