Menu Close

Prove-that-s-n-1-n-s-p-P-1-p-s-1-




Question Number 10670 by FilupS last updated on 22/Feb/17
Prove that:  ζ(s)=Σ_(n=1) ^∞ n^(−s) =Π_(p∈P) ^∞ (1−p^(−s) )^(−1)
$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\zeta\left({s}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{n}^{−{s}} =\underset{{p}\in\mathbb{P}} {\overset{\infty} {\prod}}\left(\mathrm{1}−{p}^{−{s}} \right)^{−\mathrm{1}} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *