On Recursive Hyperbolic Fibonacci Quaternions
On Recursive Hyperbolic Fibonacci Quaternions
Many quaternions with the coefficients selected from special integer sequences such as Fibonacci and Lucas sequences have been investigated by a great number of researchers. This article presents new classes of quaternions whose components are composed of symmetrical hyperbolic Fibonacci functions. In addition, the Binet's formulas, certain generating matrices, generating functions, Cassini's and d'Ocagne's identities for these quaternions are given.
Keywords:
Binet, Cassini, Generating Matrix, Hyperbolic Fibonacci functions Quaternion,
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- [1] W. R. Hamilton, Lectures on quaternions, Hodges and Smith, Dublin, 1853.
- [2] J. H. Conway, Quaternions and octonions, A K Peters/CRC Press, Canada, 2003.
- [3] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly, 70 (1963), 289-291.
- [4] M. R. Iyer, Some results on Fibonacci quaternions, Fibonacci Quart., 2 (1969), 201-210.
- [5] M. R. Iyer, A note on Fibonacci quaternions, Fibonacci Quart., 3 (1969), 225–229.
- [6] C. Flaut, V. Shpakivskyi, On generalized Fibonacci quaternions and Fibonacci–Narayana quaternions, Adv. Appl. Clifford Alg., 23 (2013), 673-688.
- [7] P. Catarino, A note on h(x)-Fibonacci quaternion polynomials, Chaos Solitons Fractals, 77 (2015), 1-5.
- [8] J. L. Ramirez, Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions, An. St. Univ. Ovidius Constanta, 23 (2015), 201-212.
- [9] A. P. Stakhov, I. S. Tkachenko, Hyperbolic Fibonacci trigonometry, Rep. Ukr. Acad. Sci., 208 (1993), 9-14.
- [10] A. P. Stakhov, Hyperbolic Fibonacci and Lucas functions: A new mathematics for the living nature, ITI, Vinnitsa, 2003.
- [11] A. P. Stakhov, B. Rozin, On a new class of hyperbolic functions, Chaos Solitons Fractals, 23 (2005), 379-389.
- [12] A. Das¸demir, On hyperbolic Lucas quaternions, Ars Combin., 150 (2020), 77-84.
- ISSN: 2651-4001
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2018
- Yayıncı: Emrah Evren KARA