Ramanujan-type identities for alternating Hurwitz zeta functions

Meng Yuan, Su Hu, Min-Soo Kim

Around 1910, in an unpublished manuscript, Ramanujan proposed the following identity for $\zeta (2n+1)$: \[ \begin{aligned} α^{-n}\,&\left\{\dfrac{1}{2}\,ζ(2n + 1) + \sum_{m = 1}^{\inft…