[sf.cmath.ellint.1]

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

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

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

#### 29.7.6.12 Incomplete elliptic integral of the first kind [sf.cmath.ellint.1]

[ð](#lib:ellint_1)

`floating-point-type ellint_1(floating-point-type k, floating-point-type phi);
float        ellint_1f(float k, float phi);
long double  ellint_1l(long double k, long double phi);
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10424)

*Effects*: These functions compute
the incomplete elliptic integral of the first kind
of their respective argumentsk and phi (phi measured in radians)[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10431)

*Returns*: F(k, Ï),
where F is given by Formula [29.32](#eq:sf.cmath.ellint.1),k is k, andÏ is phi[.](#2.sentence-1)

F(k,Ï)=â«Ï0dÎ¸â1âk2sin2Î¸Â , forÂ |k|â¤1(29.32)
