Std::hermite,std::hermitef,std::hermitel (3) Linux Manual Page

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

Synopsis

double hermite(unsigned int n, double x);

float hermite(unsigned int n, float x);

long double hermite(unsigned int n, long double x);
(1)(since C++ 17)

    float hermitef(unsigned int n, float x);

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

double hermite(unsigned int n, IntegralType x);
(2)(since C++ 17)

1) Computes the (physicist’s) Hermite_polynomials of the degree n and argument x
2) A set of overloads or a function template accepting an argument of any integral_type. Equivalent to (1) after casting the argument to double.

Parameters

n – the degree of the polynomial
x – the argument, a value of a floating-point or integral type

Return value

If no errors occur, value of the order-nHermite polynomial of x, that is (-1)n
ex2
dn
dxn
e-x2
, is returned.

Error handling

Errors may be reported as specified in math_errhandling

* If the argument is NaN, NaN is returned and domain error is not reported
* If n is greater or equal than 128, the behavior is implementation-defined

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:
* hermite(0, x) = 1

* hermite(1, x) = 2x

* hermite(2, x) = 4x2

-2

* hermite(3, x) = 8x3

-12x

* hermite(4, x) = 16x4

-48x2

+12

Example

// Run this code

#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';
}

Output:

7880=7880
155212=155212

External links

Weisstein,_Eric_W._""Hermite_Polynomial." From MathWorld–A Wolfram Web Resource.

std::hermite,std::hermitef,std::hermitel (3) Linux Manual Page