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Dirichlet eta function ( $η (s)$ )

For

ℜ s > 0

, the alternating Dirichlet series

η (s) = \sum_{n = 1}^{\infty} (- 1)^{n - 1} n^{- s}

converges locally uniformly and defines a holomorphic function. For

ℜ s > 1

,

η (s) = (1 - 2^{1 - s}) ζ (s) .

Table of contents 71 1
- Analytic continuation of the Riemann zeta function to the right half-plane Dirichlet eta function 49

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