Fibonacci-Catalan Series
Kunle Adegoke, Robert Frontczak, Taras Goy
TL;DR
This paper investigates series involving Catalan and reciprocal Catalan numbers, providing new closed-form formulas with Fibonacci and Lucas numbers, along with related combinatorial sums.
Contribution
It introduces novel closed-form evaluations of Catalan-based series using Fibonacci and Lucas numbers, and derives related combinatorial identities.
Findings
New closed-form formulas for Catalan series with Fibonacci and Lucas numbers
Derivation of combinatorial sums from the series
Insights into relationships between Catalan, Fibonacci, and Lucas numbers
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.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Advanced Mathematical Identities · Advanced Combinatorial Mathematics