One-parameter Darboux-deformed Fibonacci numbers
General Mathematics
2023-06-07 v2
Abstract
One-parameter Darboux deformations are effected for the simple ODE satisfied by the continuous generalizations of the Fibonacci sequence recently discussed by Faraoni and Atieh [Symmetry 13, 200 (2021)], who promoted a formal analogy with the Friedmann equation in the FLRW homogeneous cosmology. The method allows the introduction of deformations of the continuous Fibonacci sequences, hence of Darboux-deformed Fibonacci (non integer) numbers. Considering the same ODE as a parametric oscillator equation, the Ermakov-Lewis invariants for these sequences are also discussed.
Keywords
Cite
@article{arxiv.2212.12336,
title = {One-parameter Darboux-deformed Fibonacci numbers},
author = {H. C. Rosu and S. C. Mancas},
journal= {arXiv preprint arXiv:2212.12336},
year = {2023}
}
Comments
7 pages, 4 figures