table of contents
std::laguerre,std::laguerref,std::laguerrel(3) | C++ Standard Libary | std::laguerre,std::laguerref,std::laguerrel(3) |
NAME¶
std::laguerre,std::laguerref,std::laguerrel - std::laguerre,std::laguerref,std::laguerrel
Synopsis¶
Defined in header <cmath>
double laguerre( unsigned int n, double x );
float laguerre( unsigned int n, float x );
long double laguerre( unsigned int n, long double x ); (1) (since
C++17)
float laguerref( unsigned int n, float x );
long double laguerrel( unsigned int n, long double x );
double laguerre( unsigned int n, IntegralType x ); (2) (since
C++17)
1) Computes the non-associated Laguerre polynomials of the degree n and
argument x
2) A set of overloads or a function template accepting an argument of any
integral
type. Equivalent to (1) after casting the argument to double.
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
e^x
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¶
// Run this code
#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
See also¶
assoc_laguerre
assoc_laguerref
assoc_laguerrel associated Laguerre polynomials
(C++17) (function)
(C++17)
(C++17)
External links¶
Weisstein, Eric W. "Laguerre Polynomial." From MathWorld--A Wolfram Web Resource.
2022.07.31 | http://cppreference.com |