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

Technical specifications
Filesystem library (filesystem TS)
Library fundamentals (library fundamentals TS)
Library fundamentals 2 (library fundamentals TS v2)
Library fundamentals 3 (library fundamentals TS v3)
Extensions for parallelism (parallelism TS)
Extensions for parallelism 2 (parallelism TS v2)
Extensions for concurrency (concurrency TS)
Concepts (concepts TS)
Ranges (ranges TS)
Mathematical special functions (special functions TR)
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 );
1) Computes the associated Laguerre polynomials of the degree n, order m, and argument x
4) 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, 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.


[edit] Parameters

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

[edit] Return value

If no errors occur, value of the associated Laguerre polynomial of x, that is (-1)m
, is returned (where L
is the unassociated Laguerre polynomial, std::laguerre(n+m, x)).

[edit] 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.

[edit] 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,,
+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) =
  • assoc_laguerre(3, m, x) =

[edit] Example

(works as shown with gcc 6.0)

#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';



[edit] See also

Laguerre polynomials
(function) [edit]

[edit] External links

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