std::hermite, std::hermitef, std::hermitel
<cmath>
float hermite ( unsigned int n, float x );
(until C++23)
/* floating-point-type */ x );
<cmath>
double hermite ( unsigned int n, Integer x );
std::hermite for all cv-unqualified floating-point types as the type of the parameter x.(since C++23)[edit] Parameters
[edit] Return value
If no errors occur, value of the order-n Hermite polynomial of x, that is (-1)nex2
, 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:
7880=わ7880 155212=わ155212