[sf.cmath.assoc.laguerre]

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

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

### 29.7.6 Mathematical special functions [[sf.cmath]](sf.cmath#assoc.laguerre)

#### 29.7.6.2 Associated Laguerre polynomials [sf.cmath.assoc.laguerre]

[ð](#lib:assoc_laguerre)

`floating-point-type assoc_laguerre(unsigned n, unsigned m, floating-point-type x);
float        assoc_laguerref(unsigned n, unsigned m, float x);
long double  assoc_laguerrel(unsigned n, unsigned m, long double x);
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10009)

*Effects*: These functions compute
the associated Laguerre polynomials
of their respective argumentsn, m, and x[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10016)

*Returns*: Lmn(x),
where Lmn is given by Formula [29.22](#eq:sf.cmath.assoc.laguerre),Ln+m is given by Formula 29.37,n is n,m is m, andx is x[.](#2.sentence-1)

Lmn(x)=(â1)mdmdxmLn+m(x)Â , forÂ xâ¥0(29.22)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10030)

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