Hurwitz-Lerch type central binomial series

TL;DR

This paper introduces a generalized Hurwitz version of the central binomial series, explores its properties at integer points, and contributes to the understanding of related series in number theory.

Contribution

It defines the Hurwitz central binomial series and investigates its values at integer points, extending previous studies of the classical series.

Findings

Defined the Hurwitz central binomial series with a real parameter.

Analyzed the series' values at integer points.

Extended understanding of binomial series in number theory.

Abstract

The central binomial series is a subject that has been extensively studied, for example in the context of the irrationality of Riemann zeta values. In this paper, the Hurwitz version of the central binomial series is defined by adding one real parameter, and its values at integer points are studied.