In this work, we presented an analytical study of the generalized Fibonacci polynomial of order r ≥ 2, by using properties of the fundamental system associated with the generalized Fibonacci polynomial. We established the generating function and provided the asymptotic behavior for each system sequence. Moreover, the properties are extended to any generalized Fibonacci type, given the general case’s generating function and asymptotic behavior.
Rocha et al. (Wed,) studied this question.