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Showing content from https://en.cppreference.com/w/cpp/language/../numeric/special_functions/hermite.html below:

std::hermite, std::hermitef, std::hermitel - cppreference.com

(1) 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 );

(2) (since C++17)

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

(3) (since C++17)

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

(A) (since C++17) 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)

A) Additional overloads are provided for all integer types, which are treated as double.

[edit] Parameters n - the degree of the polynomial x - the argument, a floating-point or integer value [edit] Return value

If no errors occur, value of the order-

n

Hermite polynomial of

x

, that is

(-1)n e^x2e^-x2

, is returned.

[edit] 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.

[edit] 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:

Function Polynomial hermite(0, x) 1 hermite(1, x) 2x hermite(2, x) 4x2 - 2 hermite(3, x) 8x3 - 12x hermite(4, x) 16x4 - 48x2 + 12

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<double>(num)).

[edit] 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';
}

Output:

[edit] See also [edit] External links

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