Can one let me know about the functional equation of the alternating zeta function similar to the well known for the rieman function.



Functional equation of the alternating zeta function
Since one has 
$$\sum\_{n=1}^{\infty} \frac{(-1)^{n-1}}{n^s} = (1 -2^{1-s}) \zeta (s)$$ 
you get a Functional equation directly from the one for $\zeta$.


Note: This is function is also called [Dirichlet eta function](http://en.wikipedia.org/wiki/Dirichlet_eta_function) ; the linked Wikipedia page also has the equation spelled out. 


