On a family of infinite series with reciprocal Catalan numbers
arXiv:2201.00109
Abstract
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.
17 pages. No tables or figures