An Addendum to Plouffe's Ramanujan Identities
General Mathematics
2025-09-24 v2
Abstract
We introduce a new class of polylogarithm sums closely related to a family studied by L. Vep\v{s}tas 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.
Cite
@article{arxiv.2507.00040,
title = {An Addendum to Plouffe's Ramanujan Identities},
author = {Segun Olofin Akerele},
journal= {arXiv preprint arXiv:2507.00040},
year = {2025}
}
Comments
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