English

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

R2 v1 2026-06-28T07:50:37.157Z