Riemann Zeta Function in terms of Dirichlet Eta Function

Theorem
Let $\zeta$ be the Riemann zeta function.

Let $\eta$ be the Dirichlet eta function.

Let $s \in \C$ be a complex number with real part $\sigma > 1$.

Then:
 * $\map \zeta s = \dfrac 1 {1 - 2^{1 - s} } \map \eta s$

Also see

 * Analytic Continuation of Riemann Zeta Function using Dirichlet Eta Function