An Addendum to Plouffe's Ramanujan Identities
Segun Olofin Akerele

TL;DR
This paper introduces a new class of polylogarithm sums with parameters, providing closed-form expressions involving the Dirichlet eta function, and offers an alternative proof for a Ramanujan hyperbolic sum.
Contribution
It extends existing work by defining parameterized polylogarithm sums and connecting them to the Dirichlet eta function, along with a novel proof of a Ramanujan sum.
Findings
New class of polylogarithm sums with two parameters
Closed-form expressions involving Dirichlet eta function
Alternative proof for a Ramanujan hyperbolic sum
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Mathematical Inequalities and Applications
