[sf.cmath.cyl.neumann]

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

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

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

#### 29.7.6.11 Cylindrical Neumann functions [sf.cmath.cyl.neumann]

[ð](#lib:cyl_neumann)

`floating-point-type cyl_neumann(floating-point-type nu, floating-point-type x);
float        cyl_neumannf(float nu, float x);
long double  cyl_neumannl(long double nu, long double x);
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10370)

*Effects*: These functions compute the cylindrical Neumann functions,
also known as the cylindrical Bessel functions of the second kind,
of their respective argumentsnu and x[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10377)

*Returns*: NÎ½(x),
where NÎ½ is given by Formula [29.31](#eq:sf.cmath.cyl.neumann),Î½ is nu, andx is x[.](#2.sentence-1)

NÎ½(x)=â§âª
âª
âª
âª
âª
âª
âªâ¨âª
âª
âª
âª
âª
âª
âªâ©JÎ½(x)cosÎ½ÏâJâÎ½(x)sinÎ½Ï,forÂ xâ¥0Â and non-integralÂ Î½limÎ¼âÎ½JÎ¼(x)cosÎ¼ÏâJâÎ¼(x)sinÎ¼Ï,forÂ xâ¥0Â and integralÂ Î½(29.31)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10401)

*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#L10407)

See also [[sf.cmath.cyl.bessel.j]](sf.cmath.cyl.bessel.j "29.7.6.9 Cylindrical Bessel functions of the first kind")[.](#4.sentence-1)
