Dirichlet eta function
= Dirichlet eta function
{c}
{title2=$\eta(s)$}
{wiki}
For $\Re s>0$, the alternating <Dirichlet series>
$$
\eta(s)=\sum_{n=1}^\infty(-1)^{n-1}n^{-s}
$$
converges locally uniformly and defines a <holomorphic function>. For $\Re s>1$,
$$
\eta(s)=(1-2^{1-s})\zeta(s).
$$