std::ellint_3, std::ellint_3f, std::ellint_3l
Defined in header
float ellint_3 ( float k, float nu, float phi );
double ellint_3 ( double k, double nu, double phi );
| (since C++17)
/* floating-point-type */ ellint_3( /* floating-point-type */ k,
/* floating-point-type */ nu,
float ellint_3f( float k, float nu, float phi );
long double ellint_3l( long double k, long double nu, long double phi );
Defined in header
template< class Arithmetic1, class Arithmetic2, class Arithmetic3 >
/* common-floating-point-type */
std::ellint_3for all cv-unqualified floating-point types as the type of the parameters k, nu and phi. (since C++23)
|k||-||elliptic modulus or eccentricity (a floating-point or integer value)|
|nu||-||elliptic characteristic (a floating-point or integer value)|
|phi||-||Jacobi amplitude (a floating-point or integer value, measured in radians)|
 Return valueIf no errors occur, value of the incomplete elliptic integral of the third kind of k, nu, and phi, that is ∫phi
 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.
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.
The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their first argument num1, second argument num2 and third argument num3:
If num1, num2 and num3 have arithmetic types, then std::ellint_3(num1, num2, num3) has the same effect as std::ellint_3(static_cast</* common-floating-point-type */>(num1),
If no such floating-point type with the greatest rank and subrank exists, then overload resolution does not result in a usable candidate from the overloads provided.
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
| (complete) elliptic integral of the third kind |
|Weisstein, Eric W. "Elliptic Integral of the Third Kind." From MathWorld — A Wolfram Web Resource.|