On some Series involving Reciprocals of $\binom{2n}{n}$ and the Catalan's Constant $G$ (2411.11884v1)

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.