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

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< cpp‎ | experimental‎ | special math

double comp_ellint_3( double k, double nu ); float comp_ellint_3( float k, float nu ); long double comp_ellint_3( long double k, long double nu ); float comp_ellint_3f( float k, float nu ); long double comp_ellint_3l( long double k, long double nu ); | (1) |
double comp_ellint_3( IntegralType k, IntegralType nu ); | (2) |

1) Computes the complete elliptic integral of the third kind of `arg`.
4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to (1) after casting the argument to double.

As all special functions, `comp_ellint_3` is only guaranteed to be available in `<cmath>` 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.

### Parameters

nu | - | value of a floating-point or integral type
k | - | value of a floating-point or integral type

### Return value

If no errors occur, value of the complete elliptic integral of the second kind of `arg`, that is 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 either |k|>1 or |nu|>1, a domain error may occur

### Notes

Implementations that do not support TR 29124 but support TR 19768, provide this function in the header `tr1/cmath` and namespace `std::tr1`

An implementation of this function is also available in boost.math

### Example

(works as shown with gcc 6.0)

Run this code

    #define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
    #include <cmath>
    #include <iostream>
    int main()
    {
        double hpi = std::acos(-1)/2;
        std::cout << "Π(0, 0.75) = " << std::comp_ellint_3(0, 0.75) << '\n'
                  << "π/2 = " << hpi << '\n'
                  << "Π(0.5, 0.75) = " << std::comp_ellint_3(0.5, 0.75) << '\n'
                  << "Π(0.5, 0.75, π/2) = " << std::ellint_3(0.5, 0.75, hpi) << '\n';
    }

Output:

    Π(0, 0.75) = 3.14159
    π/2 = 1.5708
    Π(0.5, 0.75) = 3.45372
    Π(0.5, 0.75, π/2) = 3.45372

### External links

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

### See also

ellint_3 ellint_3f ellint_3l | (incomplete) elliptic integral of the third kind (function)

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