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Journals / Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 16 Sayı: 1

On Gaussianian Narayana and Gaussianian Narayana-Lucas Hybrid Numbers

Merve Taştan(TOKAT GAZİOSMANPAŞA ÜNİVERSİTESİ, ZİLE MESLEK YÜKSEKOKULU, FİNANS-BANKACILIK VE SİGORTACILIK BÖLÜMÜ)0000-0002-6001-8267
Pages
283–290
Publication Date
2026-03-01
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AI Summary & Key Takeaways

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

We also present several algebraic properties of these newly defined numbers, including their recurrence relations, Binet-type formulas, and summation identities.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Hybrid numbers, which generalize complex, hyperbolic, and dual numbers, have been the subject of extensive research to date.
📊
Key Findings & Data:In this study, we introduce the Gaussian–Narayana Hybrid and Gaussian–Narayana–Lucas Hybrid numbers by combining hybrid number theory with the Gaussian Narayana and Gaussian Narayana–Lucas sequences.
💡
Conclusion & Impact:We also present several algebraic properties of these newly defined numbers, including their recurrence relations, Binet-type formulas, and summation identities.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Hibrit sayıları · Narayana dizisi · narayana-lucas dizisi

Abstract

Hybrid numbers, which generalize complex, hyperbolic, and dual numbers, have been the subject of extensive research to date. In this study, we introduce the Gaussian–Narayana Hybrid and Gaussian–Narayana–Lucas Hybrid numbers by combining hybrid number theory with the Gaussian Narayana and Gaussian Narayana–Lucas sequences. We also present several algebraic properties of these newly defined numbers, including their recurrence relations, Binet-type formulas, and summation identities.

Özet

Karmaşık, hiperbolik ve dual sayıları genelleştiren hibrit sayılar, bugüne kadar kapsamlı araştırmaların konusu olmuştur. Bu çalışmada, hibrit sayılar teorisini Gauss-Narayana ve Gauss-Narayana-Lucas dizileriyle birleştirerek Gauss-Narayana Hibrit ve Gauss-Narayana-Lucas Hibrit sayılarını tanıtıyoruz. Ayrıca, bu yeni tanımlanan sayıların tekrarlama ilişkileri, Binet tipi formüller ve toplam özdeşlikleri de dahil olmak üzere çeşitli cebirsel özelliklerini sunuyoruz.

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Cite This Article

Taştan, M. (2026). On Gaussianian Narayana and Gaussianian Narayana-Lucas Hybrid Numbers. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 16 Sayı: 1, 283–290. https://doi.org/10.21597/jist.1744643

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