# How to compute the alternating Hurwitz zeta function?

Hi all!

What is the best way to compute the alternating Hurwitz zeta function with Sage?

Sage has an implementation of the Hurwitz zeta function, hurwitz_zeta(s,x), where s and x are complex, but not for the alternating Hurwitz zeta function.

There is the formula https://dlmf.nist.gov/25.11#E35 albeit with significant restrictions on the domain of s and x.

Which is a reliable way to implement hurwitz_alt_zeta(s,x) for general complex s and x, based on Sage functions?

A project by Fredrik Johansson FunGrim: The Mathematical Functions Grimoire is to eventually transform automatically such formula into code which respects the restrictions on the domain, etc. I don't know if it is ready yet for what you want to do or if alternating Hurwitz zeta function is in there. See this recent preprint arXiv:2003.06181