std::hermite,std::hermitef,std::hermitel (3) - Linux Manuals

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

NAME

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.