std::assoc_laguerre, std::assoc_laguerref, std::assoc_laguerrel
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) |
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/* 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>
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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)Contents |
[edit] 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 |
[edit] Return value
If no errors occur, value of the associated Laguerre polynomial of x, that is (-1)mdm |
dxm |
[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 or m is greater or equal to 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 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)] | ||
assoc_laguerre(3, m, x) |
- 3(m + 3)x2 - 3(m + 2)(m + 3)x + (m + 1)(m + 2)(m + 3)] |
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)).
[edit] 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
[edit] See also
(C++17)(C++17)(C++17) |
Laguerre polynomials (function) |
[edit] External links
Weisstein, Eric W. "Associated Laguerre Polynomial." From MathWorld — A Wolfram Web Resource. |