std::laguerre, std::laguerref, std::laguerrel

Header: <cmath>

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)

# Declarations

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 );

(since C++17)

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

(since C++17)

Additional overloads

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

(since C++17)

# Parameters

• n: the degree of the polynomial, an unsigned integer value
• x: the argument, a floating-point or integer value

# 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:

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(num)).

# 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';
}

# See also

• assoc_laguerreassoc_laguerrefassoc_laguerrel