January 1, 2025Open Access

On an analytical study of the generalized Fibonacci polynomials

Key Points

The research establishes generating functions for generalized fibonacci polynomials, allowing for further exploration of their properties.
Asymptotic behavior of each system sequence for order r ≥ 2 was analyzed, highlighting significant mathematical characteristics.
This analytical study utilizes fundamental properties of generalized fibonacci polynomials, enhancing understanding of various mathematical applications.
The findings can extend to any generalized fibonacci type, showcasing the versatility and depth of polynomial analysis.

Abstract

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.

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Cite This Study

Rocha et al. (Wed,) studied this question.

synapsesocial.com/papers/68af59e3ad7bf08b1eadebf1 https://doi.org/https://doi.org/10.7546/nntdm.2025.31.3.535-546

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