Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Fibonacci Identities via Calculus

Version 1 : Received: 4 November 2023 / Approved: 6 November 2023 / Online: 6 November 2023 (08:16:09 CET)

How to cite: Adegoke, K. Fibonacci Identities via Calculus. Preprints 2023, 2023110284. https://doi.org/10.20944/preprints202311.0284.v1 Adegoke, K. Fibonacci Identities via Calculus. Preprints 2023, 2023110284. https://doi.org/10.20944/preprints202311.0284.v1

Abstract

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 strength of our method is that no additional information is required about the given original identity. The method readily extends to a generalized Fibonacci sequence.

Keywords

Fibonacci number, Lucas number, gibonacci sequence, generalized Fibonacci sequence, summation identity, Gelin-Ces\`aro identity, Candido's identity.

Subject

Computer Science and Mathematics, Algebra and Number Theory

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