Definition:Dirichlet Eta Function
(Redirected from Definition:Alternating Zeta Function)
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Definition
The Dirichlet $\eta$ (eta) function is the complex function defined on the half-plane $\map \Re s > 0$ as the series:
- $\ds \map \eta s = \sum_{n \mathop = 1}^\infty \paren {-1}^{n - 1} n^{-s}$
Also known as
The Dirichlet $\eta$ Function is also known as the alternating $\zeta$ (zeta) function, and denoted $\map {\zeta^*} s$.
Also see
- Results about the Dirichlet $\eta$ function can be found here.
Generalizations
Source of Name
This entry was named for Johann Peter Gustav Lejeune Dirichlet.
Sources
- Weisstein, Eric W. "Dirichlet Eta Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DirichletEtaFunction.html