std::hermit...d::hermitel(3)

🌸 NAME 🌸

okay so this is the std::hermite, std::hermitef, std::hermitel page from the C++ Standard Libary manual, and the whole std::hermite,std::hermitef,std::hermitel gang is literally the main character here. 💅

🌈 Synopsis 🌈

double      hermite( unsigned int n, double x );

double      hermite( unsigned int n, float x );
double      hermite( unsigned int n, long double x );  (1)
float       hermitef( unsigned int n, float x );

long double hermitel( unsigned int n, long double x );
double      hermite( unsigned int n, IntegralType x ); (2)

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.

bestie, important vibe check: as all special functions, hermite is only guaranteed to be available in <cmath> 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.

🎀 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. no cap, that’s the whole return-value tea. 🫶

💀 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.

heads up: implementation-defined means exactly what it sounds like — do not expect a universal slay. 😭

🦋 Notes 🦋

Implementations that do not support TR 29124 but support TR 19768 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 🍓

(works as shown with gcc 6.0) — Run this code, bestie:

#define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
#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 — Laguerre polynomials
• laguerref (function)
• laguerrel
• legendre — Legendre polynomials
• legendref (function)
• legendrel

🌈 External links 🌈

• Weisstein, Eric W. ""Hermite Polynomial." From MathWorld--A Wolfram Web Resource.

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source/version: http://cppreference.com · date: 2024.06.10 — bye bestie, go compute those polynomials 💖✨