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On a generalization for fibonacci quaternions

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  • Halici, Serpil
  • Karataş, Adnan

Abstract

In this study, we introduced a quaternion sequence which has not been introduced before. We show that the new quaternion sequence that we introduced includes the previously introduced Fibonacci, Lucas, Pell, Pell–Lucas, Jacobsthal and Jacobsthal–Lucas quaternion sequences. We obtained the Binet formula and calculated the Cassini identity, summation formula and the norm value for this new quaternion sequence.

Suggested Citation

  • Halici, Serpil & Karataş, Adnan, 2017. "On a generalization for fibonacci quaternions," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 178-182.
    • Handle: RePEc:eee:chsofr:v:98:y:2017:i:c:p:178-182
    DOI: 10.1016/j.chaos.2017.03.037
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    References listed on IDEAS

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    1. Catarino, Paula, 2015. "A note on h(x) − Fibonacci quaternion polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 1-5.
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    Cited by:

    1. Ayşe Zeynep Azak, 2022. "Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions," Mathematics, MDPI, vol. 10(24), pages 1-10, December.
    2. Anatriello, Giuseppina & Németh, László & Vincenzi, Giovanni, 2022. "Generalized Pascal’s triangles and associated k-Padovan-like sequences," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 278-290.

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