Some identities for Fibonacci and Lucas polynomials via the Fibonacci Q(x)-matrix
DOI:
https://doi.org/10.17268/sel.mat.2026.01.09Keywords:
Fibonacci polynomials, Lucas polynomials, matricesAbstract
In this paper, we study Fibonacci and Lucas polynomials through the Fibonacci Q(x)-matrix. By analyzing its powers and inverses, we derive several identities for both polynomial families, including extensions to negative indices. We establish that the powers of Q(x) and their inverses have identical determinants and permanents. Furthermore, we obtain an m-term Honsberger-type identity for Fibonacci and Lucas polynomials and provide a matrix-based proof.
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