Std::laguerre,std::laguerref,std::laguerrel (3) Linux Manual Page

std::laguerre,std::laguerref,std::laguerrel – std::laguerre,std::laguerref,std::laguerrel

Synopsis

double laguerre(unsigned int n, double x);

float laguerre(unsigned int n, float x);

long double laguerre(unsigned int n, long double x);
(1)(since C++ 17)

    float laguerref(unsigned int n, float x);

long double laguerrel(unsigned int n, long double x);

double laguerre(unsigned int n, IntegralType x);
(2)(since C++ 17)

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.

Parameters

n – the degree of the polymonial, a value of unsigned integer type
x – the argument, a value of a floating-point or integral type

Return value

If no errors occur, value of the nonassociated Laguerre polynomial of x, that is
ex
n!
dn
dxn
(xn
e-x), 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 x is negative, a domain error may occur
* 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 Laguerre polynomials are the polynomial solutions of the equation xy,,

+(1-x)y,

+ny = 0

The first few are:
* laguerre(0, x) = 1

* laguerre(1, x) = -x + 1

* laguerre(2, x) =

  1
  2
  [x2
  -4x+2]
* laguerre(3, x) =
  1
  6
  [-x3
  -9×2
  -18x+6]

Example

// 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

External links

Weisstein,_Eric_W._"Laguerre_Polynomial." From MathWorld–A Wolfram Web Resource.

std::laguerre,std::laguerref,std::laguerrel (3) Linux Manual Page