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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, it is seen that the theorems and the equations which are obtained for the special values p = 1 and q = 0 correspond to the theorems and identities in [2].
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, dual-complex Fibonacci numbers with generalized Fibonacci and Lucas coefficients are dened.
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Key Findings & Data:Generating function is given for this number system.
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Conclusion & Impact:Finally, it is seen that the theorems and the equations which are obtained for the special values p = 1 and q = 0 correspond to the theorems and identities in [2].
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Dual-complex numbers · generalized Fibonacci
Abstract
In this paper, dual-complex Fibonacci numbers with generalized Fibonacci and Lucas coefficients are dened. Generating function is given for this number system. Binet formula is obtained by the help of this generating function. Then, well-known Cassini, Catalan, d'Ocagne's, Honsberger, Tagiuri and other identities are given for this number system. Finally, it is seen that the theorems and the equations which are obtained for the special values p = 1 and q = 0 correspond to the theorems and identities in [2].
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Cite This Article
CİHAN, A., AZAK, A. Z., GÜNGÖR, M. A. (2020). On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. Mathematical Sciences and Applications E-Notes, Cilt: 8 - Sayı: 1, 55–68. https://ajindex.com/articles/283458