std::laguerre, std::laguerref, std::laguerrel
<cmath>
double laguerre ( unsigned int n, double x );
(until C++23)
/* floating-point-type */ x );
<cmath>
double laguerre ( unsigned int n, Integer x );
std::laguerre for all cv-unqualified floating-point types as the type of the parameter x.(since C++23)[edit] Parameters
[edit] Return value
If no errors occur, value of the nonassociated Laguerre polynomial of x, that ise-x), is returned.
[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 is greater or equal than 128, the behavior is implementation-defined
[edit] 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 .
The first few are:
| Function | Polynomial |
|---|---|
| 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) |
The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::laguerre(int_num, num) has the same effect as std::laguerre(int_num, static_cast<double>(num)).
[edit] Example
#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' << std::laguerre(3, 0.0) << '=' << 1.0 << '\n'; }
Output:
0.5=0.5 0.125=0.125 1=1