[sf.cmath.comp.ellint.3]

# 29 Numerics library [[numerics]](./#numerics)

## 29.7 Mathematical functions for floating-point types [[c.math]](c.math#sf.cmath.comp.ellint.3)

### 29.7.6 Mathematical special functions [[sf.cmath]](sf.cmath#comp.ellint.3)

#### 29.7.6.7 Complete elliptic integral of the third kind [sf.cmath.comp.ellint.3]

[ð](#lib:comp_ellint_3)

`floating-point-type comp_ellint_3(floating-point-type k, floating-point-type nu);
float        comp_ellint_3f(float k, float nu);
long double  comp_ellint_3l(long double k, long double nu);
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10190)

*Effects*: These functions compute
the complete elliptic integral of the third kind
of their respective argumentsk and nu[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10197)

*Returns*: Î (Î½,k),
where Î  is given by Formula [29.27](#eq:sf.cmath.comp.ellint.3),k is k, andÎ½ is nu[.](#2.sentence-1)

Î (Î½,k)=Î (Î½,k,Ï/2)Â , forÂ |k|â¤1(29.27)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10207)

See also [[sf.cmath.ellint.3]](sf.cmath.ellint.3 "29.7.6.14 Incomplete elliptic integral of the third kind")[.](#3.sentence-1)
