On a family of infinite series with reciprocal Catalan numbers

2022/01/01 by Kunle Adegoke, Robert Frontczak, Adegoke, Kunle +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2201.00109

openalex publication_date 2022/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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