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Showing content from https://en.cppreference.com/w/cpp/language/../algorithm/../numeric/special_functions/laguerre.html below:

std::laguerre, std::laguerref, std::laguerrel - cppreference.com

(1) float laguerre ( unsigned int n, float x ); double laguerre ( unsigned int n, double x ); long double laguerre ( unsigned int n, long double x ); (since C++17)
(until C++23)

/* floating-point-type */ laguerre( unsigned int n, /* floating-point-type */ x );

(since C++23)

float laguerref( unsigned int n, float x );

(2) (since C++17)

long double laguerrel( unsigned int n, long double x );

(3) (since C++17)

template< class Integer > double laguerre ( unsigned int n, Integer x );

(A) (since C++17) 1-3)

Computes the non-associated

Laguerre polynomials

of the degree

n

and argument

x

The library provides overloads of std::laguerre for all cv-unqualified floating-point types as the type of the parameter x.(since C++23)

A) Additional overloads are provided for all integer types, which are treated as double.

[edit] Parameters n - the degree 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 nonassociated Laguerre polynomial of

x

, that is

(xn e^-x)

, is returned.

[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 is greater or equal than 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 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) 1 2 (x2 - 4x + 2) laguerre(3, x) 1 6 (-x3 - 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 argument num of integer type, std::laguerre(int_num, num) has the same effect as std::laguerre(int_num, static_cast<double>(num)).

[edit] Example

#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:

[edit] See also [edit] External links

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