Eta Function Formula
\zeta(s)=\frac{1}{1-2^{1-s}}\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n^s}=\frac{\eta(s)}{1-2^{1-s}}
A simple formula connecting the Riemann Zeta function to the Dirichlet Eta function.
It requires a very manageable demonstration, but has non-trivial implications: It represents one of the most basic ways to extend the function to the halfplane Re(s)>0 and gives information on the sign of the function for some particular cases.
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