std::assoc_laguerre, std::assoc_laguerref, std::assoc_laguerrel

double      assoc_laguerre ( unsigned int n, unsigned int m, double x );
double      assoc_laguerre ( unsigned int n, unsigned int m, float x );
double      assoc_laguerre ( unsigned int n, unsigned int m, long double x );
float       assoc_laguerref( unsigned int n, unsigned int m, float x );
long double assoc_laguerrel( unsigned int n, unsigned int m, long double x );

double      assoc_laguerre ( unsigned int n, unsigned int m, IntegralType x );

As all special functions, assoc_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 associated Laguerre polynomial of x, that is

, is returned (where Ln + m(x) is the unassociated Laguerre polynomial, std::laguerre(n + m, x)).

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 or m is greater or equal to 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 associated Laguerre polynomials are the polynomial solutions of the equation xy,,
+ (m + 1 - x)y,
+ ny = 0.

The first few are:

• assoc_laguerre(0, m, x) = 1.
• assoc_laguerre(1, m, x) = -x + m + 1.
• assoc_laguerre(2, m, x) =

  1

  2

  [x2
  - 2(m + 2)x + (m + 1)(m + 2)].
• assoc_laguerre(3, m, x) =

  1

  6

  [-x3
  - 3(m + 3)x2
  - 3(m + 2)(m + 3)x + (m + 1)(m + 2)(m + 3)].

Example

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

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

double L2(unsigned m, double x)
{
    return 0.5 * (x * x - 2 * (m + 2) * x + (m + 1) * (m + 2));
}

int main()
{
    // spot-checks
    std::cout << std::assoc_laguerre(1, 10, 0.5) << '=' << L1(10, 0.5) << '\n'
              << std::assoc_laguerre(2, 10, 0.5) << '=' << L2(10, 0.5) << '\n';
}

10.5=10.5
60.125=60.125

See also

External links