Sum and weighted sum formulas for fibonacci and lucas quaternions
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Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Aksaray Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Fibonacci and Lucas quaternions are deeply studied in the literature after its definition by Horadam in 1963. Binet formula, generation function, Cassini, Catalan, Honsberger, and other identities for these sequences studied in different quaternion algebra types like split quaternion algebra, dual quaternion algebra, etc. Additionally, some of the generalizations for Fibonacci and Lucas quaternions are studied like k-Fibonacci quaternions, k-Lucas quaternions, Horadam quaternions, and more. However, despite being researched intensively, the summation formulas or weighted summation formulas for these sequences are not examined thoroughly. In this study, after briefly summarizing the literature, we focused on the summation and the weighted summation formulas for the Fibonacci and the Lucas quaternions. In addition, we provided generalized weighted summation formulas for the Fibonacci and Lucas quaternions. Moreover, we calculated generalized weighted summation formulas for the double coefficient Fibonacci and double coefficient Lucas quaternions which have two Fibonacci and Lucas coefficient in every unit of the quaternion, respectively.
Açıklama
Anahtar Kelimeler
Fibonacci Numbers, Lucas Numbers, Sum Formulas, Weighted Sum Formulas, Double Coefficient Fibonacci Numbers
Kaynak
Aksaray University Journal of Science and Engineering (ASUJSE)
WoS Q Değeri
Scopus Q Değeri
Cilt
8
Sayı
2
