On the bicomplex Gaussian Fibonacci and Gaussian Lucas numbers

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Kuloğlu B., ÖZKAN E.

Acta et Commentationes Universitatis Tartuensis de Mathematica, cilt.26, sa.1, ss.33-43, 2022 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 26 Sayı: 1
• Basım Tarihi: 2022
• Doi Numarası: 10.12697/acutm.2022.22.03
• Dergi Adı: Acta et Commentationes Universitatis Tartuensis de Mathematica
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier
• Sayfa Sayıları: ss.33-43
• Anahtar Kelimeler: Bicomplex numbers, Gaussian Fibonacci numbers, bicomplex Gaussian Fibonacci numbers, Binet's formula
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• Marmara Üniversitesi Adresli: Hayır

Özet

We give the bicomplex Gaussian Fibonacci and the bicomplex Gaussian Lucas numbers and establish the generating functions and Binet’s formulas related to these numbers. Also, we present the summation formula, matrix representation and Honsberger identity and their relationship between these numbers. Finally, we show the relationships among the bicomplex Gaussian Fibonacci, the bicomplex Gaussian Lucas, Gaussian Fibonacci, Gaussian Lucas and Fibonacci numbers.