[sf.cmath.ellint.2]

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

## 29.7 Mathematical functions for floating-point types [[c.math]](c.math#sf.cmath.ellint.2)

### 29.7.6 Mathematical special functions [[sf.cmath]](sf.cmath#ellint.2)

#### 29.7.6.13 Incomplete elliptic integral of the second kind [sf.cmath.ellint.2]

[ð](#lib:ellint_2)

`floating-point-type ellint_2(floating-point-type k, floating-point-type phi);
float        ellint_2f(float k, float phi);
long double  ellint_2l(long double k, long double phi);
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10457)

*Effects*: These functions compute
the incomplete elliptic integral of the second 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#L10464)

*Returns*: E(k, Ï),
where E is given by Formula [29.33](#eq:sf.cmath.ellint.2),k is k, andÏ is phi[.](#2.sentence-1)

E(k,Ï)=â«Ï0â1âk2sin2Î¸dÎ¸Â , forÂ |k|â¤1(29.33)
