Sums of series involving central binomial coefficients & harmonic numbers

TL;DR

This paper explores series involving central binomial coefficients and harmonic numbers, deriving elegant sums that include the Riemann zeta function and other interesting series.

Contribution

It introduces new series involving binomial coefficients and harmonic numbers, and presents elegant closed-form sums including zeta functions.

Findings

Derived new series involving central binomial coefficients and harmonic numbers

Presented an elegant sum involving ζ(2) and other series

Connected series sums to special functions like the Riemann zeta function

Abstract

This paper contains a number of series whose coefficients are products of central binomial coefficients & harmonic numbers. An elegant sum involving $\zeta(2)$ and two other nice sums appear in the last section.