Dual Fibonacci Quaternions
Semra Kaya Nurkan, \.Ilkay Arslan G\"uven
TL;DR
This paper introduces dual Fibonacci and Lucas quaternions, establishing their mathematical relations and deriving formulas like Binet and Cassini for these new quaternion types.
Contribution
It defines dual Fibonacci and Lucas quaternions and derives their fundamental relations and formulas, extending Fibonacci and Lucas number concepts into quaternion algebra.
Findings
Defined dual Fibonacci and Lucas quaternions
Derived relations between these quaternions and Fibonacci/Lucas numbers
Established Binet and Cassini formulas for the new quaternions
Abstract
In this study, we define the dual Fibonacci quaternion and the dual Lucas quternion. We derive the relations between the dual Fibonacci and the dual Lucas quaternion which connected the Fibonacci and the Lucas numbers. Furthermore, we give the Binet and Cassini formulas for these quaternions.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Advanced Mathematical Theories · Biofield Effects and Biophysics