NAME¶

std::ellint_3,std::ellint_3f,std::ellint_3l - std::ellint_3,std::ellint_3f,std::ellint_3l

Synopsis¶

Defined in header <cmath>
double ellint_3( double k, double ν, double φ );

float ellint_3f( float k, float ν, float φ ); (1) (since C++17)

long double ellint_3l( long double k, long double ν, long double
φ );
Promoted ellint_3( Arithmetic k, Arithmetic ν, Arithmetic φ ); (2) (since C++17)

1) Computes the incomplete elliptic integral of the third kind of k, ν, and φ.
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)
φ - Jacobi amplitude (a value of floating-point or integral type, measured in
radians)

Return value¶

If no errors occur, value of the incomplete elliptic integral of the third kind of
k, ν, and φ, that is ∫φ
0

dθ
(1-νsin2
θ)
√
1-k2
sin2
θ

, 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()
{
double hpi = std::acos(-1)/2;
std::cout << "Π(0,0,π/2) = " << std::ellint_3(0, 0, hpi) << '\n'
<< "π/2 = " << hpi << '\n';
}

Output:¶

Π(0,0,π/2) = 1.5708
π/2 = 1.5708

This section is incomplete
Reason: this and other elliptic integrals deserve better examples.. perhaps
calculate elliptic arc length?

See also¶

comp_ellint_3
comp_ellint_3f
comp_ellint_3l (complete) 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.