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

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

double      laguerre( unsigned int n, IntegralType x );

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.

Parameters

Return value

If no errors occur, value of the nonassociated Laguerre polynomial of x, that is

, 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 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:

• 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

#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';
}

0.5=0.5
0.125=0.125

See also

External links

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