Difference between revisions of "Dirichlet eta"
From specialfunctionswiki
(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...") |
(s -> z) |
||
| (9 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
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}.$$ |
| − | + | ||
| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Dirichletetaplot.png|Graph of $\eta$. | ||
| + | File:Complexdirichletetaplot.png|[[Domain coloring]] of $\eta$. | ||
| + | </gallery> | ||
| + | </div> | ||
| + | |||
| + | =See Also= | ||
| + | [[Riemann zeta]]<br /> | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 20:58, 5 November 2017
Let $\mathrm{Re} \hspace{2pt} z > 0$, then define $$\eta(z) = \displaystyle\sum_{n=1}^{\infty} \dfrac{(-1)^{n-1}}{n^z}.$$
Graph of $\eta$.
Domain coloring of $\eta$.
