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A note on h(x) − Fibonacci quaternion polynomials

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  • Catarino, Paula

Abstract

In this paper, we introduce h(x) − Fibonacci quaternion polynomials that generalize the k − Fibonacci quaternion numbers, which in their turn are a generalization of the Fibonacci quaternion numbers. We also present a Binet-style formula, ordinary generating function and some basic identities for the h(x) − Fibonacci quaternion polynomial sequences.

Suggested Citation

  • Catarino, Paula, 2015. "A note on h(x) − Fibonacci quaternion polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 1-5.
    • Handle: RePEc:eee:chsofr:v:77:y:2015:i:c:p:1-5
    DOI: 10.1016/j.chaos.2015.04.017
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    References listed on IDEAS

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    1. Nalli, Ayse & Haukkanen, Pentti, 2009. "On generalized Fibonacci and Lucas polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3179-3186.
    2. Stakhov, Alexey & Rozin, Boris, 2005. "The Golden Shofar," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 677-684.
    3. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
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    Cited by:

    1. Can Kızılateş & Emrah Polatlı, 2021. "New families of Fibonacci and Lucas octonions with $$Q-$$ Q - integer components," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(1), pages 231-240, March.
    2. Tan, Elif & Yilmaz, Semih & Sahin, Murat, 2016. "On a new generalization of Fibonacci quaternions," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 1-4.
    3. Kızılateş, Can, 2020. "A new generalization of Fibonacci hybrid and Lucas hybrid numbers," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Tan, Elif & Yilmaz, Semih & Sahin, Murat, 2016. "A note on bi-periodic Fibonacci and Lucas quaternions," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 138-142.
    5. Halici, Serpil & Karataş, Adnan, 2017. "On a generalization for fibonacci quaternions," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 178-182.

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