@article{article_1117644, title={Gaussian Quaternions Including Biperiodic Fibonacci and Lucas Numbers}, journal={Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi}, volume={6}, pages={594–604}, year={2023}, DOI={10.47495/okufbed.1117644}, author={Gökbaş, Hasan}, keywords={Quaternion, Gaussian quaternion, Bi-periodic Fibonacci ve Lucas sayıları}, 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.}, number={1}, publisher={Osmaniye Korkut Ata Üniversitesi}