std::ellint_3, std::ellint_3f, std::ellint_3l
double ellint_3( double k, double ν, double φ );
float ellint_3f( float k, float ν, float φ );
Promoted ellint_3( Arithmetic k, Arithmetic ν, Arithmetic φ );
Promotedis also long double, otherwise the return type is always double.
|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 valueIf no errors occur, value of the incomplete elliptic integral of the third kind of
φ, that is ∫φ
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
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
An implementation of this function is also available in boost.math
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?
Weisstein, Eric W. "Elliptic Integral of the Third Kind." From MathWorld--A Wolfram Web Resource.
| (complete) elliptic integral of the third kind |