1
$\begingroup$

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

$\endgroup$

1 Answer 1

6
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.