Gaussian Quaternions Including Biperiodic Fibonacci and Lucas Numbers

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Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Volume:6 Issue:1
Gaussian Quaternions Including Biperiodic Fibonacci and Lucas Numbers

Gaussian Quaternions Including Biperiodic Fibonacci and Lucas Numbers

Pages : 594-604

View : 95 | Download : 18

Publication Date : 2023-03-10

Article Type : Research Paper

Abstract :In this study, we define a type of bi-periodic Fibonacci and Lucas numbers which are called bi-periodic Fibonacci and Lucas Gaussian quaternions. We also give the relationship between negabi-periodic Fibonacci and Lucas Gaussian quaternions and bi-periodic Fibonacci and Lucas Gaussian quaternions. Moreover, we obtain the Binet’s formula, generating function, d’Ocagne’s identity, Catalan’s identity, Cassini’s identity, like-Tagiuri’s identity, Honberger’s identity and some formulas for these new type numbers. Some algebraic proporties of bi-periodic Fibonacci and Lucas Gaussian quaternions which are connected between Gaussian quaternions and bi-periodic Fibonacci and Lucas numbers are investigated.
Keywords : Quaternion, Gaussian quaternion, Bi periodic Fibonacci ve Lucas sayıları

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