Difference between revisions of "Dirichlet eta"
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This series is clearly the [[Riemann zeta function]] with alternating terms. | This series is clearly the [[Riemann zeta function]] with alternating terms. | ||
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| + | File:Complex Dirichlet eta function.jpg|[[Domain coloring]] of [[domain coloring]] of $\eta(z)$. | ||
| + | </gallery> | ||
| + | </div> | ||
| + | [[500px]] | ||
Revision as of 23:20, 1 April 2015
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 $\eta(z)$.
