The Relationship Between Generalized Fibonacci Polynomials

In this study, we obtain the relationship between two different generalized Fibonacci polynomials ($F_{k,n}(t)$ and $F_{k,n}(s)$). We discuss some of the special cases of $F_{k,n}(t)$ and $F_{k,n}(s)$, and we show that the obtained results are valid in these special cases. Since $F_{k,n}(s)$ is a new polynomial obtained by a different selection of the coefficients of the core polynomial used to define $F_{k,n}(t)$, our results will provide a new perspective on this issue. This perspective allows us to generalize classical results, such as the relationship between number sequences, the connection between this relationship and the coefficients of the core polynomial, and the method of obtaining these sequences using matrices.