std:: comp_ellint_3, std:: comp_ellint_3f, std:: comp_ellint_3l

From cppreference.com
C++
Numerics library
Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Data-parallel types ( simd ) (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array ( valarray )
Pseudo-random number generation
Factor operations
(C++17)
(C++17)
Interpolations
(C++20)
(C++20)
Saturation arithmetic
(C++26)
(C++26)
(C++26)
(C++26)
(C++26)

Generic numeric operations
Bit operations
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
Mathematical special functions
Defined in header <cmath>
(1)
float comp_ellint_3 ( float k, float nu ) ;

double comp_ellint_3 ( double k, double nu ) ;

long double comp_ellint_3 ( long double k, long double nu ) ;
(since C++17)
(until C++23)
/* floating-point-type */ comp_ellint_3 ( /* floating-point-type */ k,
/* floating-point-type */ nu ) ;
(since C++23)
float comp_ellint_3f ( float k, float nu ) ;
(2) (since C++17)
long double comp_ellint_3l ( long double k, long double nu ) ;
(3) (since C++17)
Defined in header <cmath>
template < class Arithmetic1, class Arithmetic2 >

/* common-floating-point-type */

comp_ellint_3 ( Arithmetic1 k, Arithmetic2 nu ) ;
(A) (since C++17)
1-3) Computes the complete elliptic integral of the third kind of the arguments k and nu . The library provides overloads of std::comp_ellint_3 for all cv-unqualified floating-point types as the type of the parameters k and nu . (since C++23)
A) Additional overloads are provided for all other combinations of arithmetic types.

Parameters

k - elliptic modulus or eccentricity (a floating-point or integer value)
nu - elliptic characteristic (a floating-point or integer value)

Return value

If no errors occur, value of the complete elliptic integral of the third kind of k and nu , that is std:: ellint_3 ( k, nu, π / 2 ) , is returned.

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 |k|>1 , a domain error may occur

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 additional overloads are not required to be provided exactly as (A) . They only need to be sufficient to ensure that for their first argument num1 and second argument num2 :

  • If num1 or num2 has type long double , then std :: comp_ellint_3 ( num1, num2 ) has the same effect as std :: comp_ellint_3 ( static_cast < long double > ( num1 ) ,
    static_cast < long double > ( num2 ) )     .
  • Otherwise, if num1 and/or num2 has type double or an integer type, then std :: comp_ellint_3 ( num1, num2 ) has the same effect as std :: comp_ellint_3 ( static_cast < double > ( num1 ) ,
    static_cast < double > ( num2 ) )     .
  • Otherwise, if num1 or num2 has type float , then std :: comp_ellint_3 ( num1, num2 ) has the same effect as std :: comp_ellint_3 ( static_cast < float > ( num1 ) ,
    static_cast < float > ( num2 ) )     .
(until C++23)

If num1 and num2 have arithmetic types, then std :: comp_ellint_3 ( num1, num2 ) has the same effect as std :: comp_ellint_3 ( static_cast < /* common-floating-point-type */ > ( num1 ) ,
static_cast < /* common-floating-point-type */ > ( num2 ) ) , where /* common-floating-point-type */ is the floating-point type with the greatest floating-point conversion rank and greatest floating-point conversion subrank between the types of num1 and num2 , arguments of integer type are considered to have the same floating-point conversion rank as double .

If no such floating-point type with the greatest rank and subrank exists, then overload resolution does not result in a usable candidate from the overloads provided.

(since C++23)

Example

Run this code 
#include <cmath>
#include <iostream>
 
int main()
{
    std::cout << std::fixed
              << "Π(0.5,0) = " << std::comp_ellint_3(0.5, 0) << '\n'
              << "K(0.5)   = " << std::comp_ellint_1(0.5) << '\n'
              << "Π(0,0)   = " << std::comp_ellint_3(0, 0) << '\n'
              << "π/2      = " << std::acos(-1) / 2 << '\n'
              << "Π(0.5,1) = " << std::comp_ellint_3(0.5, 1) << '\n';
}

Output: 

Π(0.5,0) = 1.685750
K(0.5)   = 1.685750
Π(0,0)   = 1.570796
π/2      = 1.570796
Π(0.5,1) = inf

See also

(C++17) (C++17) (C++17)
(incomplete) elliptic integral of the third kind
(function)

External links

Weisstein, Eric W. "Elliptic Integral of the Third Kind." From MathWorld — A Wolfram Web Resource.
Retrieved from " https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/special_functions/comp_ellint_3&oldid=149506 "