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One-parameter Darboux-deformed Fibonacci numbers

H.C. RosuS.C. Mancas
Dec 2022
摘要
One-parameter Darboux deformations are effected for the simple ODE satisfiedby the continuous generalizations of the Fibonacci sequence recently discussedby Faraoni and Atieh [Symmetry 13, 200 (2021)], who promoted a formal analogywith the Friedmann equation in the FLRW homogeneous cosmology. The methodallows the introduction of deformations of the continuous Fibonacci sequences,hence of Darboux-deformed Fibonacci (non integer) numbers. Considering the sameODE as a parametric oscillator equation, the Ermakov-Lewis invariants for thesesequences are also discussed.
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