On a new generalization of Fibonacci quaternions. (English) Zbl 1355.11013
Summary: In this paper, we present a new generalization of the Fibonacci quaternions that are emerged as a generalization of the best known quaternions in the literature, such as classical Fibonacci quaternions, Pell quaternions, \(k\)-Fibonacci quaternions. We give the generating function and the Binet formula for these quaternions. By using the Binet formula, we obtain some well-known results. Also, we correct some results in [P. Catarino, Chaos Solitons Fractals 77, 1–5 (2015; Zbl 1353.11021)] and [C. B. Çimen and A. İpek, Adv. Appl. Clifford Algebr. 26, No. 1, 39–51 (2016; Zbl 1344.11022)] which have been overlooked that the quaternion multiplication is non-commutative.
MSC:
| 11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |
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