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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We also obtain some generalization of well – known identities such as Catalan’s, Cassini’s and d’Ocagne’s identities.
📌 3 Key Takeaways
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Objective & Hypothesis:In this study, we define unrestricted Pell and Pell – Lucas hyper-complex numbers.
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Key Findings & Data:We choose arbitrary Pell and Pell – Lucas numbers for the coefficients of the ordered basis 〖{e〗_0,e_1,⋯,e_(N-1)} of hyper-complex 2^N-ons where N∈{0,1,2,3,4} and call these hyper-complex numbers unrestricted Pell and Pell-Lucas 2N-ons.
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Conclusion & Impact:We also obtain some generalization of well – known identities such as Catalan’s, Cassini’s and d’Ocagne’s identities.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Pell sequence · Pell-Lucas sequence · Quaternion
Abstract
In this study, we define unrestricted Pell and Pell – Lucas hyper-complex numbers. We choose arbitrary Pell and Pell – Lucas numbers for the coefficients of the ordered basis 〖{e〗_0,e_1,⋯,e_(N-1)} of hyper-complex 2^N-ons where N∈{0,1,2,3,4} and call these hyper-complex numbers unrestricted Pell and Pell-Lucas 2N-ons. We give generating functions and Binet formulas for these type of hyper-complex numbers. We also obtain some generalization of well – known identities such as Catalan’s, Cassini’s and d’Ocagne’s identities.
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Cite This Article
Özsoy, Ö. B., Bilgici, G. (2022). Unrestricted Pell and Pell – Lucas 2N-ons. Kocaeli Journal of Science and Engineering, Cilt: 5 Sayı: 2, 112–116. https://doi.org/10.34088/kojose.1033409