std::assoc_laguerre, std::assoc_laguerref, std::
Defined in header <cmath>
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| (1) | ||
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float assoc_laguerre (
unsigned
int n, unsigned
int m, float x )
;
double assoc_laguerre (
unsigned
int n, unsigned
int m, double x )
;
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(since C++17) (until C++23) |
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/* floating-point-type */ assoc_laguerre(
unsigned
int n, unsigned
int m,
/* floating-point-type */ x ) ; |
(since C++23) | |
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float assoc_laguerref(
unsigned
int n, unsigned
int m, float x )
;
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(2) | (since C++17) |
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long
double assoc_laguerrel(
unsigned
int n, unsigned
int m, long
double x )
;
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(3) | (since C++17) |
Defined in header <cmath>
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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| dm |
| dxm |
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__
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) |
- 2(m + 2)x + (m + 1)(m + 2)] |
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| assoc_laguerre(3, m, x) |
- 3(m + 3)x2 |
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
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(C++17)(C++17)(C++17)
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Laguerre polynomials (function) |
External links
| Weisstein, Eric W. "Associated Laguerre Polynomial." From MathWorld — A Wolfram Web Resource. |