Difference between revisions of "Dirichlet eta"
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Let $\mathrm{Re} \hspace{2pt} z > 0$, then define | Let $\mathrm{Re} \hspace{2pt} z > 0$, then define | ||
| − | $$\eta(z) = \displaystyle\sum_{n=1}^{\infty} \dfrac{(-1)^{n-1}}{n^ | + | $$\eta(z) = \displaystyle\sum_{n=1}^{\infty} \dfrac{(-1)^{n-1}}{n^z}.$$ |
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<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
File:Dirichletetaplot.png|Graph of $\eta$. | File:Dirichletetaplot.png|Graph of $\eta$. | ||
| − | File: | + | File:Complexdirichletetaplot.png|[[Domain coloring]] of $\eta$. |
</gallery> | </gallery> | ||
</div> | </div> | ||
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=See Also= | =See Also= | ||
[[Riemann zeta]]<br /> | [[Riemann zeta]]<br /> | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 20:58, 5 November 2017
Let $\mathrm{Re} \hspace{2pt} z > 0$, then define $$\eta(z) = \displaystyle\sum_{n=1}^{\infty} \dfrac{(-1)^{n-1}}{n^z}.$$
Graph of $\eta$.
Domain coloring of $\eta$.
