- Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Vol: 6 Issue: 1
- Gaussian Quaternions Including Biperiodic Fibonacci and Lucas Numbers
Gaussian Quaternions Including Biperiodic Fibonacci and Lucas Numbers
Authors : Hasan Gökbaş
Pages : 594-604
Doi:10.47495/okufbed.1117644
View : 6 | Download : 5
Publication Date : 2023-03-10
Article Type : Research
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