Dirichlet’s Eta Function
Calculate the values of the Dirichlet eta function η(x) and 1 - η(x).
| \(\normalsize\ Dirichlet\ Eta\ function\ \eta(x)\\ (1)\ \eta(x)= {\large\displaystyle \sum_{\small n=1}^ {\small\infty}\frac{(-1)^{n-1}}{n^x}}\\ (2)\ \eta(x)=(1-2^{1-x})\zeta(x),\hspace{30px} \zeta(x)= {\large\displaystyle \sum_{\small n=1}^ {\small\infty}\frac{1}{n^x}}\\ (3)\ \eta(1)=\ln2\\ \) |
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