Dirichlet eta

From specialfunctionswiki
Revision as of 05:37, 19 October 2014 by Tom (talk | contribs)
Jump to: navigation, search

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.

500px