Fibonacci-Catalan Series

2022/04/09 by Kunle Adegoke, Robert Frontczak, Adegoke, Kunle +3 · 1 citation
Mathematics · Physics and Astronomy · #11B37 #11B39 #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.2204.04535

openalex publication_date 2022/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study certain series with Catalan numbers and reciprocal Catalan numbers, respectively, and provide seemingly new closed form evaluations of these series with Fibonacci (Lucas) entries. In addition, we state some combinatorial sums that can be inferred from the series.

Cited by

• On Some Series Involving the Central Binomial Coefficients
• Explicit Identities and new results for Infinite Series associated with the Ratio of Central Binomial Coefficients

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• Catalan numbers, Hankel determinants and Fibonacci polynomials
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• Generalizations for reciprocal Fibonacci-Lucas sums of Brousseau
• On some Series involving Reciprocals of \binom2nn and the Catalan's Constant G