std::hermite, std::hermitef, std::hermitel
Defined in header <cmath>
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(1) | ||
double hermite ( unsigned int n, double x ); float hermite ( unsigned int n, float x ); |
(since C++17) (until C++23) |
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/* 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) |
Defined in header <cmath>
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template< class Integer > double hermite ( unsigned int n, Integer x ); |
(A) | (since C++17) |
std::hermite
for all cv-unqualified floating-point types as the type of the parameter x.(since C++23)Contents |
[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)nex2
dn |
dxn |
, 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=7880 155212=155212
[edit] See also
(C++17)(C++17)(C++17) |
Laguerre polynomials (function) |
(C++17)(C++17)(C++17) |
Legendre polynomials (function) |
[edit] External links
Weisstein, Eric W. "Hermite Polynomial." From MathWorld — A Wolfram Web Resource. |