[sf.cmath.riemann.zeta]

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

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

### 29.7.6 Mathematical special functions [[sf.cmath]](sf.cmath#riemann.zeta)

#### 29.7.6.19 Riemann zeta function [sf.cmath.riemann.zeta]

[ð](#lib:riemann_zeta)

`floating-point-type riemann_zeta(floating-point-type x);
float        riemann_zetaf(float x);
long double  riemann_zetal(long double x);
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10671)

*Effects*: These functions compute the Riemann zeta function
of their respective argumentsx[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10677)

*Returns*: Î¶(x),
where Î¶ is given by Formula [29.39](#eq:sf.cmath.riemann.zeta) andx is x[.](#2.sentence-1)

Î¶(x)=â§âª
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âªâ©ââk=1kâx,forÂ x>111â21âxââk=1(â1)kâ1kâx,forÂ 0â¤xâ¤12xÏxâ1sin(Ïx2)Î(1âx)Î¶(1âx),forÂ x<0(29.39)
