Quaternions via generalized Fibonacci and Lucas number components
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Tarih
2019
Yazarlar
Dergi Başlığı
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Cilt Başlığı
Yayıncı
Editura Acad Romane
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this paper, we derive some combinatorial properties of generalized Fibonacci quaternion Q(n) and generalized Lucas quaternion K-n, where the components of Q(n) and K-n are generalized Fibonacci number U-n and generalized Lucas number V-n, respectively. Firstly, we obtain some basic identities and use them to prove Catalan identity for Q(n) and K-n. Then we find some sum formulas Sigma(n)(i=0)Qmi+r, Sigma(n)(i=0)Kmi+r, Sigma(n)(i=0)((n)(i))p(i) q(n-i)Q(i) and Sigma(n)(i=0)((n)(i))p(i) q(n-i)K(i) in terms of Q(n) and K-n. Moreover, we derive the generating functions of these generalized quaternions.
Açıklama
Anahtar Kelimeler
generalized Fibonacci numbers, generalized Lucas numbers, generalized quaternions, generating functions
