2 papers
math.GM2026
Arctanh Sums: Analytic Continuation and Prime-Restricted Theory
Ryan Goulden
We study the arctanh sums h(k) = sum_{n=2}^\infty arctanh(n^{-k}) as a function of a complex variable k. Building on the closed-form identity h(k) = (1/2) log(g(2k)/g(k)^2) (proved…
math.GM2026
Closed-Form Evaluation of Arctanh Power Sums via Infinite Products
Ryan Goulden
We establish closed-form expressions for the infinite series sum from n=2 to infinity of arctanh(n^-k) for all integers k >= 2 by connecting these sums to infinite product formulas…