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Sums of Products of $s$-Fibonacci
Polynomial Sequences Claudio de Jesús Pita Ruiz Velasco
Universidad Panamericana
Mexico City, Mexico
mailto:cpita@up.edu.mxcpita@up.edu.mx

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Abstract:

We consider $s$-Fibonacci polynomial sequences $\left( F_{0}\left( x\right) ,F_{s}\left( x\right) ,F_{2s}\left( x\right) ,\ldots \right)$, where $s\in \mathbb{N}$ is given. By studying certain $z$-polynomials involving $s$-polyfibonomials $\binom{n}{k}_{\!F_{s}\left( x\right) }\!\!=\frac{% F_{sn}\left( x\right) \cdot... ...right) }\left( x\right) }{% F_{s}\left( x\right) \cdots F_{ks}\left( x\right) }$ and $s$-Gibonacci polynomial sequences $\left( G_{0}\left( x\right) ,G_{s}\left( x\right) ,G_{2s}\left( x\right) ,\ldots \right)$, we generalize some known results (and obtain some new results) concerning sums of products and addition formulas of Fibonacci numbers.