Difference between revisions of "Dirichlet eta"
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(Created page with "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...") |
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$$\eta(z) = \displaystyle\sum_{n=1}^{\infty} \dfrac{(-1)^{n-1}}{n^s}.$$ | $$\eta(z) = \displaystyle\sum_{n=1}^{\infty} \dfrac{(-1)^{n-1}}{n^s}.$$ | ||
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|500px]] | ||
Revision as of 05:37, 19 October 2014
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.
