An Addendum to Plouffe's Ramanujan Identities

2025/06/19 by Segun Olofin Akerele, Akerele, Segun Olofin
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.2507.00040

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.

Citations

• On a problem of Mező and its generalizations to three classes of rational zeta series
• Some infinite series involving hyperbolic functions
• Identities inspired by the Ramanujan Notebooks, second series

Related

• Extensions of Euler Type Sums and Ramanujan Type Sums
• A series of Ramanujan, two-term dilogarithm identities and some Lucas series
• On Sum-Of-Tails Identities
• Explicit formulas of a generalized Ramanujan sum
• On a series of Ramanujan, dilogarithm values, and solitons