# 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)
Additional overloads |  |
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

ellint_2 ellint_2f ellint_2l (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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