std::laguer...d::laguerrel(3)

💅 std::laguerre, std::laguerref, std::laguerrel 💅

okay bestie, welcome to the C++ Standard Library manual page std::laguer...d::laguerrel(3) — yes, the title has that little ... moment and we are simply living with it. this page is all about the Laguerre polynomial girlies. 💖

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🌸 NAME 🌸

std::laguerre,std::laguerref,std::laguerrel — std::laguerre,std::laguerref,std::laguerrel

✨ Synopsis ✨

double      laguerre( unsigned int n, double x );

double      laguerre( unsigned int n, float x );
double      laguerre( unsigned int n, long double x );  (1)
float       laguerref( unsigned int n, float x );

long double laguerrel( unsigned int n, long double x );
double      laguerre( unsigned int n, IntegralType x ); (2)

1. Computes the non-associated Laguerre 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.

As all special functions, laguerre 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. read the preprocessor tea leaves first, bestie. ☕️

💖 Parameters 💖

• n — the degree of the polynomial, a value of unsigned integer type.
• x — the argument, a value of a floating-point or integral type.

🦋 Return value 🦋

If no errors occur, the value of the nonassociated Laguerre polynomial of x, that is e^x / n! times d^n/dx^n (x^n e^-x), is returned. slay. 💫

😭 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 x is negative, a domain error may occur.
• If n is greater or equal than 128, the behavior is implementation-defined. this is the part where you do not act surprised, okay? 💀

🧚 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 Laguerre polynomials are the polynomial solutions of the equation xy'' + (1 - x)y' + ny = 0.

The first few are, literally as printed:

• laguerre(0, x) = 1.
• laguerre(1, x) = -x + 1.
• laguerre(2, x) = 1/2 [x2 - 4x + 2].
• laguerre(3, x) = 1/6 [-x3 - 9x2 - 18x + 6].

🔥 Example 🔥

(works as shown with gcc 6.0)

// Run this code

#define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
#include <cmath>
#include <iostream>

double L1(double x)
{
    return -x + 1;
}

double L2(double x)
{
    return 0.5 * (x * x - 4 * x + 2);
}

int main()
{
    // spot-checks
    std::cout << std::laguerre(1, 0.5) << '=' << L1(0.5) << '\n'
              << std::laguerre(2, 0.5) << '=' << L2(0.5) << '\n';
}

Output:

0.5=0.5
0.125=0.125

👑 See also 👑

• assoc_laguerre — associated Laguerre polynomials
• assoc_laguerref — (function)
• assoc_laguerrel

🌈 External links 🌈

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

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and that’s the tea, bestie 🫶 this iconic little page comes from cppreference.com, dated 2024.06.10, and its page title is std::laguer...d::laguerrel(3). periodt. 💅✨