Vipul: Created page with '==Definition== The '''Dirichlet eta-function''' is defined as the meromorphic function given by the following Dirichlet series: $\eta(s) = \sum_{n \in \mathbb{N}} ...'$

2009-05-07T01:40:52Z

Created page with '==Definition== The '''Dirichlet eta-function''' is defined as the meromorphic function given by the following Dirichlet series: <math>\eta(s) = \sum_{n \in \mathbb{N}} ...'

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==Definition==

The '''Dirichlet eta-function''' is defined as the [[meromorphic function]] given by the following [[Dirichlet series]]:

<math>\eta(s) = \sum_{n \in \mathbb{N}} \frac{(-1)^{n-1}}{n^s}</math>.

It can also be defined in terms of the [[defining ingredient::Riemann zeta-function]] as:

<math>\eta(s) = (1 - 2^{1 - s})\zeta(s)</math>.

==Relation with other functions==

* [[Riemann zeta-function]]

Dirichlet eta-function - Revision history

Vipul: Created page with '==Definition== The '''Dirichlet eta-function''' is defined as the meromorphic function given by the following Dirichlet series: \eta(s) = \sum_{n \in \mathbb{N}} ...'

Vipul: Created page with '==Definition== The '''Dirichlet eta-function''' is defined as the meromorphic function given by the following Dirichlet series: $\eta(s) = \sum_{n \in \mathbb{N}} ...'$