Sums of Products of s-Fibonacci Polynomial Sequences

We consider

-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

-polynomials involving

-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

-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.

Sums of Products of s-Fibonacci Polynomial Sequences

Claudio de Jesús Pita Ruiz Velasco Universidad Panamericana Mexico City, Mexico

Claudio de Jesús Pita Ruiz Velasco
Universidad Panamericana
Mexico City, Mexico