Difference between revisions of "Dirichlet eta"
From specialfunctionswiki
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| + | File:Dirichletetaplot.png|Graph of $\eta$. | ||
File:Complex Dirichlet eta function.jpg|[[Domain coloring]] of [[domain coloring]] of $\eta(z)$. | File:Complex Dirichlet eta function.jpg|[[Domain coloring]] of [[domain coloring]] of $\eta(z)$. | ||
</gallery> | </gallery> | ||
Revision as of 07:29, 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 $\eta$.
- Complex Dirichlet eta function.jpg
Domain coloring of domain coloring of $\eta(z)$.
