Difference between revisions of "Dirichlet eta"
From specialfunctionswiki
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File:Dirichletetaplot.png|Graph of $\eta$. | File:Dirichletetaplot.png|Graph of $\eta$. | ||
| − | File: | + | File:Complexdirichletetaplot.png|[[Domain coloring]] of $\eta$. |
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Revision as of 07:32, 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.
Graph of $\eta$.
Domain coloring of $\eta$.
