2023/11/03 by Kunle Adegoke, Adegoke, Kunle
Mathematics · Physics and Astronomy · #11B37 #11B39 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2311.06287
openalex publication_date 2023/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a differential-calculus-based method which allows one to derive more identities from \it any given Fibonacci-Lucas identity containing a finite number of terms and having at least one free index. The method has two \it independent components. The first component allows new identities to be obtained directly from an existing identity while the second yields a generalization of the existing identity. The strength of the first component is that no additional information is required about the given original identity. We illustrate the method by providing new generalizations of some well-known identities such as d'Ocagne identity, Candido's identity, Gelin-Cesàro identity and Catalan's identity. The method readily extends to a generalized Fibonacci sequence.