On a Weighted Series of the Hurwitz Zeta Function

Matthew Fox, Chaitanya Karamchedu

In this note we prove that for all $a\in \mathbb{N}$, $x\in {\mathbb{R}}_{+}\cup \{0\}$, and $s\in \mathbb{C}$ with $\Re (s)>a+2$, the (alternating) weighted series of the Hurwi…