Year: 2023
Type: preprint
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 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.
Source: arXiv (Cornell University)
Author: Adegoke, Kunle
Institution: Obafemi Awolowo University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4388684546