On k-Fibonacci sequences and polynomials and their derivatives

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Fibonacci wavelets and Galerkin method to investigate fractional optimal control problems with bibliometric analysis (2020, methodology): “…ffiffiffiffiffiffi wm p is used to normalize Fibonacci wavelets, where wm ¼ Z 1 0 ~F2mðtÞdt Moreover, Fibonacci polynomials ~FmðtÞ are defined as follows (Falcón and Plaza, 2009) ~FmðtÞ ¼ Xbm=2c i¼0 m i i tm 2i; m ≥ 0; (9) An arbitrary function f(t) 2 C[0, 1) can be approximated using the…”
On generalized Fibonacci and Lucas polynomials (2009, background): “Introduction In modern science there is a huge interest in the theory and application of the Golden Section and Fibonacci numbers [1–34].”
Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions (2015, background): “The interested reader is also referred to [2, 3, 4, 5, 6, 7, 22, 23, 24, 25], for further information about these sequences.”