std:: assoc_laguerre, std:: assoc_laguerref, std:: assoc_laguerrel
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Defined in header
<cmath>
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||
| (1) | ||
|
float
assoc_laguerre
(
unsigned
int
n,
unsigned
int
m,
float
x
)
;
double
assoc_laguerre
(
unsigned
int
n,
unsigned
int
m,
double
x
)
;
|
(since C++17)
(until C++23) |
|
|
/* floating-point-type */
assoc_laguerre
(
unsigned
int
n,
unsigned
int
m,
/* floating-point-type */ x ) ; |
(since C++23) | |
|
float
assoc_laguerref
(
unsigned
int
n,
unsigned
int
m,
float
x
)
;
|
(2) | (since C++17) |
|
long
double
assoc_laguerrel
(
unsigned
int
n,
unsigned
int
m,
long
double
x
)
;
|
(3) | (since C++17) |
|
Defined in header
<cmath>
|
||
|
template
<
class
Integer
>
double assoc_laguerre ( unsigned int n, unsigned int m, Integer x ) ; |
(A) | (since C++17) |
std::assoc_laguerre
for all cv-unqualified floating-point types as the type of the parameter
x
.
(since C++23)
Parameters
| n | - | the degree of the polynomial, an unsigned integer value |
| m | - | the order of the polynomial, an unsigned integer value |
| x | - | the argument, a floating-point or integer value |
Return value
If no errors occur, value of the associated Laguerre polynomial of x , that is (-1) m| d m |
| dx m |
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 or m is greater or equal to 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 associated Laguerre polynomials are the polynomial solutions of the equation xy ,, +(m+1-x)y , +ny = 0 .
The first few are:
| Function | Polynomial | ||
|---|---|---|---|
| assoc_laguerre ( 0 , m, x ) | 1 | ||
| assoc_laguerre ( 1 , m, x ) | -x + m + 1 | ||
| assoc_laguerre ( 2 , m, x ) |
|
||
| assoc_laguerre ( 3 , m, x ) |
|
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 :: assoc_laguerre ( int_num1, int_num2, num ) has the same effect as std :: assoc_laguerre ( int_num1, int_num2, static_cast < double > ( num ) ) .
Example
#include <cmath> #include <iostream> double L1(unsigned m, double x) { return -x + m + 1; } double L2(unsigned m, double x) { return 0.5 * (x * x - 2 * (m + 2) * x + (m + 1) * (m + 2)); } int main() { // spot-checks std::cout << std::assoc_laguerre(1, 10, 0.5) << '=' << L1(10, 0.5) << '\n' << std::assoc_laguerre(2, 10, 0.5) << '=' << L2(10, 0.5) << '\n'; }
Output:
10.5=10.5 60.125=60.125
See also
|
(C++17)
(C++17)
(C++17)
|
Laguerre polynomials
(function) |
External links
| Weisstein, Eric W. "Associated Laguerre Polynomial." From MathWorld — A Wolfram Web Resource. |