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¶

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 ); (1)
float comp_ellint_3f( float k, float nu );

long double comp_ellint_3l( long double k, long double nu );
double comp_ellint_3( IntegralType k, IntegralType nu ); (2)

1) Computes the complete elliptic integral of the third kind of arg.
2) 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 (incomplete) elliptic integral of the third kind
ellint_3f (function)
ellint_3l