29 Numerics library [numerics]

29.9 Mathematical functions for floating-point types [c.math]

29.9.5 Mathematical special functions [sf.cmath]

29.9.5.18 Riemann zeta function [sf.cmath.riemann_zeta]

double riemann_zeta(double x); float riemann_zetaf(float x); long double riemann_zetal(long double x);

1
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Effects: These functions compute the Riemann zeta function of their respective arguments x.

2
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Returns:

ζ(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩∞∑k=1k−x,for x>111−21−x∞∑k=1(−1)k−1k−x,for 0≤x≤12xπx−1sin(πx2)Γ(1−x)ζ(1−x),for x<0

where x is x.