Series Involving the Zeta Functions and a Family of Generalized Goldbach–Euler Series

Abstract

We first present the corrected expression for a certain widely-recorded generalized Goldbach–Euler series. The corrected forms are then shown to be connected with the problem of closed-form evaluation of series involving the Zeta functions, which happens to be an extensively-investigated subject since the time of Euler as (for example) in the classical three-century-old Goldbach theorem.