On some Series involving Reciprocals of $\binom{2n}{n}$ and the Catalan's Constant $G$

TL;DR

This paper explores combinatorial series involving reciprocals of central binomial coefficients and the Catalan's constant, using generating functions and integral methods to derive new identities.

Contribution

It introduces novel identities for series involving reciprocals of binomial coefficients and the Catalan's constant, expanding the analytical tools in combinatorial series.

Findings

Derived new identities for series involving reciprocals of binomial coefficients.

Connected series involving the Catalan's constant with generating functions.

Provided integral representations for these series.

Abstract

We investigate a class of combinatorial sums involving reciprocals of central binomial coefficients , employing generating functions as the primary solution technique to formulate and analyze series involving the Catalan's constant. Using a direct approach, we derive new identities through integral techniques.