On a Family of Infinite Series with Reciprocal Catalan Numbers - Kunle Adegoke; Robert Frontczak; Taras Goy (Axioms, 2022)
We study a certain family of infinite series with reciprocal Catalan numbers. We first evaluate two special candidates of the family in closed form, where we also present some Catalan–Fibonacci relations. Then, we focus on the general properties of the family and prove explicit formulas, including two types of integral representations.