Gaussian Quaternion Involving Leonardo Numbers
DOI:
https://doi.org/10.5644/SJM.19.02.06Keywords:
Gaussian quaternion, quaternion, Fibonacci numbers, Leonardo numbersAbstract
In this study, using the Leonardo numbers, we define a new type of quaternion that is called a Leonard Gaussian quaternion. We also give a negative-Leonardo Gaussian quaternion. These numbers are introduced from the set of complex numbers and quaternions. Moreover, we obtain the Binet’s formula, generating function formula, d’Ocagne’s identity, Catalan’s identity, Cassini’s identity, Honsberger’s identity, like-Vajda’s identity and some formulas for these new types of numbers. Morever, we give the matrix representation of the Leonardo Gaussian quaternion.
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