Comment on "Hybrid deformed algebra", by Andre A. Marinho, Francisco A. Brito [arXiv:1904.07843]

Abstract

In this note, we show that the $\mu$-oscillator does not lead to the Fibonacci sequence as claimed in \cite{Marinho:2019zny} since $[n]^{\mu}=n$ in the limit $\mu \rightarrow 0$. Thus we obtain the sequence $[0]^{\mu}=0, 1, 2,...$. We only obtain the Fibonacci sequence when the $q$-deformation is associated to the $\mu$-deformation via the basis number $$\lim_{\mu\rightarrow 0} [n]^{\mu}_{q_1, q_2} = \frac{q_1^{2n}-q_2^{2n}}{q_1^2-q_2^2}.$$