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Journals / Fundamental Journal of Mathematics and Applications / 2026 / Volume: 4 Issue: 1

Unrestricted Fibonacci and Lucas quaternions

Ahmet Daşdemir(KASTAMONU UNIVERSITY)0000-0001-8352-2020
Göksal Bilgici(KASTAMONU UNIVERSITY)0000-0001-9964-5578
Pages
—
Publication Date
2021-03-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also present some properties, including the Binet's formulas and d'Ocagne's identities, for these types of quaternions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Many quaternion numbers associated with Fibonacci and Lucas numbers or even their generalizations have been defined and widely discussed so far.
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Key Findings & Data:In all the studies, the coefficients of these quaternions have been selected from consecutive terms of these numbers.
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Conclusion & Impact:We also present some properties, including the Binet's formulas and d'Ocagne's identities, for these types of quaternions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fibonacci quaternion · Lucas quaternion · Binet's formula

Abstract

Many quaternion numbers associated with Fibonacci and Lucas numbers or even their generalizations have been defined and widely discussed so far. In all the studies, the coefficients of these quaternions have been selected from consecutive terms of these numbers. In this study, we define other generalizations for the usual Fibonacci and Lucas quaternions. We also present some properties, including the Binet's formulas and d'Ocagne's identities, for these types of quaternions.

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Cite This Article

Daşdemir, A., Bilgici, G. (2021). Unrestricted Fibonacci and Lucas quaternions. Fundamental Journal of Mathematics and Applications, Volume: 4 Issue: 1. https://doi.org/10.33401/fujma.752758

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