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

Yıl 2022, Cilt: 10 Sayı: 2, 282 - 292, 31.10.2022

Arzu Özkoç

Öz

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.

Anahtar Kelimeler

Binomial transform, hybrid numbers, Lucas sequences of …rst and second kind.

Kaynakça

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