[sf.cmath.cyl.bessel.k]

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

## 29.7 Mathematical functions for floating-point types [[c.math]](c.math#sf.cmath.cyl.bessel.k)

### 29.7.6 Mathematical special functions [[sf.cmath]](sf.cmath#cyl.bessel.k)

#### 29.7.6.10 Irregular modified cylindrical Bessel functions [sf.cmath.cyl.bessel.k]

[ð](#lib:cyl_bessel_k)

`floating-point-type cyl_bessel_k(floating-point-type nu, floating-point-type x);
float        cyl_bessel_kf(float nu, float x);
long double  cyl_bessel_kl(long double nu, long double x);
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10308)

*Effects*: These functions compute
the irregular modified cylindrical Bessel functions
of their respective argumentsnu and x[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10315)

*Returns*: KÎ½(x),
where KÎ½ is given by Formula [29.30](#eq:sf.cmath.cyl.bessel.k),Î½ is nu, andx is x[.](#2.sentence-1)

KÎ½(x)=(Ï/2)iÎ½+1(JÎ½(ix)+iNÎ½(ix))=â§âª
âª
âª
âª
âª
âª
âªâ¨âª
âª
âª
âª
âª
âª
âªâ©Ï2IâÎ½(x)âIÎ½(x)sinÎ½Ï,forÂ xâ¥0Â and non-integralÂ Î½Ï2limÎ¼âÎ½IâÎ¼(x)âIÎ¼(x)sinÎ¼Ï,forÂ xâ¥0Â and integralÂ Î½(29.30)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10345)

*Remarks*: The effect of calling each of these functions
is implementation-defined
if nu >= 128[.](#3.sentence-1)

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10351)

See also [[sf.cmath.cyl.bessel.i]](sf.cmath.cyl.bessel.i "29.7.6.8 Regular modified cylindrical Bessel functions"), [[sf.cmath.cyl.bessel.j]](sf.cmath.cyl.bessel.j "29.7.6.9 Cylindrical Bessel functions of the first kind"), [[sf.cmath.cyl.neumann]](sf.cmath.cyl.neumann "29.7.6.11 Cylindrical Neumann functions")[.](#4.sentence-1)
