A New Generalization of the Alternating Harmonic Series

Abstract

Kilmer and Zheng (2021) recently introduced a generalized version of the alternating harmonic series. In this paper, we introduce a new generalization of the alternating harmonic series. A special case of our generalization converges to the Kilmer-Zheng series. Then we investigate several interesting and useful properties of this generalized, such as a summation formula related to the Hurwitz -Lerch Zeta function, a duplication formula, an integral representation, derivatives, and the recurrence relationship. Some important special cases of the main results are also discussed.