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Defined in header <cmath> | ||
| (1) | ||
float laguerre(unsignedint n,float x); double laguerre(unsignedint n,double x); | (since C++17) (until C++23) | |
/* floating-point-type */ laguerre(unsignedint n, /* floating-point-type */ x); | (since C++23) | |
float laguerref(unsignedint n,float x); | (2) | (since C++17) |
longdouble laguerrel(unsignedint n,longdouble x); | (3) | (since C++17) |
Defined in header <cmath> | ||
template<class Integer> double laguerre(unsignedint n, Integer x); | (A) | (since C++17) |
std::laguerre for all cv-unqualified floating-point types as the type of the parameterx.(since C++23)Contents |
| n | - | the degree of the polynomial, an unsigned integer value |
| x | - | the argument, a floating-point or integer value |
| ex |
| n! |
| dn |
| dxn |
Errors may be reported as specified inmath_errhandling
Implementations that do not support C++17, but supportISO 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 headertr1/cmath and namespacestd::tr1.
An implementation of this function is alsoavailable 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) |
- 4x + 2) | ||
| laguerre(3, x) |
- 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 argumentnum of integer type,std::laguerre(int_num, num) has the same effect asstd::laguerre(int_num,static_cast<double>(num)).
#include <cmath>#include <iostream> double L1(double x){return-x+1;} double L2(double x){return0.5*(x* x-4* x+2);} int main(){// spot-checksstd::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=0.50.125=0.1251=1
(C++17)(C++17)(C++17) | associated Laguerre polynomials (function)[edit] |
| Weisstein, Eric W. "Laguerre Polynomial." From MathWorld — A Wolfram Web Resource. |
