table of contents
std::hermite,std::hermitef,std::hermitel(3) | C++ Standard Libary | std::hermite,std::hermitef,std::hermitel(3) |
NAME¶
std::hermite,std::hermitef,std::hermitel - std::hermite,std::hermitef,std::hermitel
Synopsis¶
Defined in header <cmath>
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-n Hermite polynomial of x,
that is (-1)n
e^x2
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
See also¶
laguerre
laguerref
laguerrel Laguerre polynomials
(C++17) (function)
(C++17)
(C++17)
legendre
legendref
legendrel Legendre polynomials
(C++17) (function)
(C++17)
(C++17)
External links¶
Weisstein, Eric W. "Hermite Polynomial." From MathWorld--A Wolfram Web Resource.
2022.07.31 | http://cppreference.com |