[sf.cmath.sph.neumann]

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

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

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

#### 29.7.6.22 Spherical Neumann functions [sf.cmath.sph.neumann]

[ð](#lib:sph_neumann)

`floating-point-type sph_neumann(unsigned n, floating-point-type x);
float        sph_neumannf(unsigned n, float x);
long double  sph_neumannl(unsigned n, long double x);
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10804)

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

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10811)

*Returns*: nn(x),
where nn is given by Formula [29.42](#eq:sf.cmath.sph.neumann),n is n, andx is x[.](#2.sentence-1)

nn(x)=(Ï/2x)1/2Nn+1/2(x)Â , forÂ xâ¥0(29.42)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10822)

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

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10828)

See also [[sf.cmath.cyl.neumann]](sf.cmath.cyl.neumann "29.7.6.11 Cylindrical Neumann functions")[.](#4.sentence-1)
