Difference between revisions of "Dirichlet eta"
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Revision as of 07:14, 24 May 2016
Let $\mathrm{Re} \hspace{2pt} z > 0$, then define $$\eta(z) = \displaystyle\sum_{n=1}^{\infty} \dfrac{(-1)^{n-1}}{n^s}.$$ This series is clearly the Riemann zeta function with alternating terms.
- Complex Dirichlet eta function.jpg
Domain coloring of domain coloring of $\eta(z)$.
