NAME¶

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

Synopsis¶

Defined in header <cmath>
double comp_ellint_3( double k, double ν );

float comp_ellint_3f( float k, float ν ); (1) (since C++17)

long double comp_ellint_3l( long double k, long double ν );
Promoted comp_ellint_3( Arithmetic k, Arithmetic ν ); (2) (since C++17)

1) Computes the complete elliptic integral of the third kind of the arguments k and
ν.
2) A set of overloads or a function template for all combinations of arguments of
arithmetic type not covered by (1). If any argument has integral type, it is cast to
double. If any argument is long double, then the return type Promoted is also long
double, otherwise the return type is always double.

Parameters¶

k - elliptic modulus or eccentricity (a value of a floating-point or integral type)
ν - elliptic characteristic (a value of floating-point or integral type)

Return value¶

If no errors occur, value of the complete elliptic integral of the third kind of k
and ν, that is std::ellint_3(k,ν,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.

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¶

ellint_3
ellint_3f
ellint_3l (incomplete) elliptic integral of the third kind
(C++17) (function)
(C++17)
(C++17)

External links¶

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