Definition:Dirichlet Eta Function

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Definition

The Dirichlet $\eta$ (eta) function $\eta$ is the complex function defined on the half-plane $\map \Re s > 0$ as the series:

$\displaystyle \map \eta s = \sum_{n \mathop = 1}^\infty \paren {-1}^{n - 1} n^{-s}$


Also known as

It is also known as the alternating $\zeta$ (zeta) function.


Also see

  • Results about Dirichlet $\eta$ function can be found here.


Generalizations


Source of Name

This entry was named for Johann Peter Gustav Lejeune Dirichlet.


Sources