An Addendum to Plouffe's Ramanujan Identities

Abstract

We introduce a new class of polylogarithm sums closely related to a family studied by L. Vepštas in 2010. These generalized sums depend on two free parameters and yield closed-form expressions involving the Dirichlet eta function. Additionally, we present an alternative proof for a hyperbolic sum originally discussed by Ramanujan.

I am withdrawing this paper because the identities employed hold only when the parameter $\alpha$ is extremely small. As a result, the lemmas and conclusions stated are not valid in the general case, and I do not wish to mislead readers