A note on bi-periodic Fibonacci and Lucas quaternions

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• 作者：Elif Tan ; ^a ; ^{etan@ankara.edu.tr" class="auth_mail" title="E-mail the corresponding author} ; Semih Yilmaz^b ; ^{syilmaz@kku.edu.tr" class="auth_mail" title="E-mail the corresponding author} ; Murat Sahin^a ; ^{msahin@ankara.edu.tr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Lucas sequence ; Generalized Lucas sequence ; Recurrence relations ; Quaternions
• 刊名：Chaos, Solitons & Fractals
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：85
• 期：Complete
• 页码：138-142
• 全文大小：321 K

文摘

Motivated by the our recent work in Tan et al., 2016, related to the bi-periodic Fibonacci quaternions, here we introduce the bi-periodic Lucas quaternions that gives the Lucas quaternions as a special case. We give the generating function and the Binet formula for these quaternions. Also, we give the relationships between bi-periodic Fibonacci quaternions and bi-periodic Lucas quaternions.