[sf.cmath.comp.ellint.1]

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

## 29.7 Mathematical functions for floating-point types [[c.math]](c.math#sf.cmath.comp.ellint.1)

### 29.7.6 Mathematical special functions [[sf.cmath]](sf.cmath#comp.ellint.1)

#### 29.7.6.5 Complete elliptic integral of the first kind [sf.cmath.comp.ellint.1]

[ð](#lib:comp_ellint_1)

`floating-point-type comp_ellint_1(floating-point-type k);
float        comp_ellint_1f(float k);
long double  comp_ellint_1l(long double k);
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10124)

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

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10131)

*Returns*: K(k),
where K is given by Formula [29.25](#eq:sf.cmath.comp.ellint.1) andk is k[.](#2.sentence-1)

K(k)=F(k,Ï/2)Â , forÂ |k|â¤1(29.25)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10140)

See also [[sf.cmath.ellint.1]](sf.cmath.ellint.1 "29.7.6.12 Incomplete elliptic integral of the first kind")[.](#3.sentence-1)
