# 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 ); (1) (since C++17) double      laguerre( unsigned int n, Integral x ); (2) (since C++17)
1) Computes the non-associated Laguerre polynomials of the degree n 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.

## Contents

### 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
-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';
}

Output:

0.5=0.5
0.125=0.125