double ellint_3( double k, double ν, double φ ); float ellint_3f( float k, float ν, float φ ); long double ellint_3l( long double k, long double ν, long double φ ); | (1) | (since C++17) |

Promoted ellint_3( Arithmetic k, Arithmetic ν, Arithmetic φ ); | (2) | (since C++17) |

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`

.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) |

`k`

, `ν`

, and `φ`

, that is ∫φ0

dθ |

(1-νsin2 θ)√1-k2 sin2 θ |

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 `std::tr1`

.

An implementation of this function is also available in boost.math.

#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

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

(C++17)(C++17)(C++17) | (complete) elliptic integral of the third kind (function) |

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