Gauss Narayana ve Gauss Narayana-Lucas Hibrit sayıları

Abstract

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.

Keywords

• Hibrit sayıları
• Narayana dizisi
• narayana-lucas dizisi

On Gaussianian Narayana and Gaussianian Narayana-Lucas Hybrid Numbers

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.

Keywords

• Hybrid numbers
• Narayana numbers
• Narayana-Lucas numbers

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