Abstract

Dairesel-hiperbolik Fibonacci ve Lucas kuaterniyonlarının bazı özelliklerini araştırıyoruz (kısaca $\mathbb{CH}FLQ $ ile gösterilen). Ayrıca negatif indislilerini tanıtıyoruz ve kombinatorik toplamlarını elde ediyoruz. Son olarak bu $\mathbb{CH}FLQ$ kuaterniyonlarının genel bir toplamını, üstel ve Poisson üreteçleri sunuyoruz.

Keywords

• binom katsayısı
• dairesel-hiperbolik Fibonacci kuaterniyonları
• dairesel-hiperbolik Lucas kuaterniyonları
• hiperbolik sayılar.

A study on circular-hyperbolic Fibonacci and Lucas quaternions

Abstract

We investigate some properties of circular-hyperbolic Fibonacci and Lucas quaternions ($\mathbb{CH}FLQ$ for short), we introduce their negative subscripts and obtain several combinatorial sums. Finally, we present a general summation, exponential and Poisson generating functions of the $\mathbb{CH}FLQ$.

Keywords

• binomial coefficient
• circular-hyperbolic Fibonacci quaternions
• circular-hyperbolic Lucas quaternions
• hyperbolic numbers.

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