One-parameter Darboux-deformed Fibonacci numbers

H. C. Rosu; S. C. Mancas

doi:10.1142/s0217732323500220

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arXiv · 2212.12336

One-parameter Darboux-deformed Fibonacci numbers

H. C. Rosu·S. C. Mancas

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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.

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BibTeX RIS

H. C. Rosu, S. C. Mancas. 2022-12-05. One-parameter Darboux-deformed Fibonacci numbers. https://doi.org/10.1142/s0217732323500220

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