std:: comp_ellint_2, std:: comp_ellint_2f, std:: comp_ellint_2l

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Defined in header <cmath>
(1)
float comp_ellint_2 ( float k ) ;

double comp_ellint_2 ( double k ) ;

long double comp_ellint_2 ( long double k ) ;
(since C++17)
(until C++23)
/* floating-point-type */ comp_ellint_2 ( /* floating-point-type */ k ) ;
(since C++23)
float comp_ellint_2f ( float k ) ;
(2) (since C++17)
long double comp_ellint_2l ( long double k ) ;
(3) (since C++17)
Defined in header <cmath>
template < class Integer >
double comp_ellint_2 ( Integer k ) ;
(A) (since C++17)
1-3) Computes the complete elliptic integral of the second kind of k . The library provides overloads of std::comp_ellint_2 for all cv-unqualified floating-point types as the type of the parameter k . (since C++23)
A) Additional overloads are provided for all integer types, which are treated as double .

Parameters

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

Return value

If no errors occur, value of the complete elliptic integral of the second kind of k , that is std::ellint_2(k, 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 perimeter of an ellipse with eccentricity k and semimajor axis a equals 4aE(k) , where E is std::comp_ellint_2 . When eccentricity equals 0 , the ellipse degenerates to a circle with radius a and the perimeter equals 2πa , so E(0) = π/2 . When eccentricity equals 1 , the ellipse degenerates to a line of length 2a, whose perimeter is 4a , so E(1) = 1 .

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 :: comp_ellint_2 ( num ) has the same effect as std :: comp_ellint_2 ( static_cast < double > ( num ) ) .

Example

Run this code 
#include <cmath>
#include <iostream>
#include <numbers>
 
int main()
{
    constexpr double hpi = std::numbers::pi / 2.0;
 
    std::cout << "E(0) = " << std::comp_ellint_2(0) << '\n'
              << "π/2 = " << hpi << '\n'
              << "E(1) = " << std::comp_ellint_2(1) << '\n'
              << "E(1, π/2) = " << std::ellint_2(1, hpi) << '\n';
}

Output: 

E(0) = 1.5708
π/2 = 1.5708
E(1) = 1
E(1, π/2) = 1

See also

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

External links

Weisstein, Eric W. "Complete Elliptic Integral of the Second Kind." From MathWorld — A Wolfram Web Resource.
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