Binomial Transforms for Hybrid Numbers Defined Through Fibonacci and Lucas Number Components

Authors : Arzu ÖZKOÇ

Pages : 282-292

View : 18 | Download : 14

Publication Date : 2022-10-31

Article Type : Research Paper

Abstract :The main purpose of covering this article has been to examine the hybrid numbers defined through Fibonacci and Lucas number components $\{\hat{H}% _{U,n}\}$ and $\{\hat{H}_{V,n}\}$~and their binomial transforms $\{b\hat{H}% _{U,n}\}$ and $\{b\hat{H}_{V,n}\},$ respectively. Firstly, general sum formulas, binomial identities, which are not in the literature yet, about hybrid numbers $\{\hat{H}_{U,n}\}$ and $\{\hat{H}_{V,n}\}$ are discussed. Then, the recurrence relation is obtained for $\{b\hat{H}_{U,n}\}$ and $\{b% \hat{H}_{V,n}\}$ and some results have been found for the new sequence.
Keywords : Binomial transform, hybrid numbers, Lucas sequences of …rst and second kind