Take the tour ×  Can one let me know about the functional
equation of the alternating zeta function similar to the well
known for the rieman function.  share|improve this question add
comment  1 Answer  up vote 6 down vote accepted  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 ; the linked Wikipedia page also has the equation
spelled out.  share|improve this answer add comment  Your Answer