Difference between revisions of "Dirichlet eta"

From specialfunctionswiki
Jump to: navigation, search
Line 5: Line 5:
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
 +
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.

See Also

Riemann zeta