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, Integral x );

Parameters

Return value

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
  -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.