# eta

eta(x)

Dirichlet eta function $\eta(s) = \sum^\infty_{n=1}(-)^{n-1}/n^{s}$.

## Examples

julia> eta(1)
-0.5772156649015329

julia> eta(2)
0.8224670334241132

julia> eta(0.5)
-0.20788622497735404

The eta function in Julia calculates the Dirichlet eta function, denoted as η(s). It takes a complex number s as input and returns the value of the Dirichlet eta function evaluated at s.

Here are some examples of using the eta function:

1. Calculate eta(1):

julia> eta(1)
-0.5772156649015329

Evaluates the Dirichlet eta function at s = 1, which returns approximately -0.5772156649015329.

2. Calculate eta(2):

julia> eta(2)
0.8224670334241132

Calculates the Dirichlet eta function at s = 2, resulting in approximately 0.8224670334241132.

3. Calculate eta(0.5):
julia> eta(0.5)
-0.20788622497735404

Computes the Dirichlet eta function at s = 0.5, which gives approximately -0.20788622497735404.

The Dirichlet eta function is defined as follows:

$\eta(s) = \sum^{\infty}_{n=1} (-1)^{n-1} \frac{1}{n^s}$

Please note that the Dirichlet eta function is defined for complex numbers s.