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Some remarks regarding h(x) – Fibonacci polynomials in an arbitrary algebra

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  • Flaut, Cristina
  • Shpakivskyi, Vitalii
  • Vlad, Elena

Abstract

In this paper, we introduce h(x) – Fibonacci polynomials in an arbitrary finite-dimensional unitary algebra over a field K(K=R,C). These polynomials generalize h(x) – Fibonacci quaternion polynomials andh(x) – Fibonacci octonion polynomials. For h(x) – Fibonacci polynomials in an arbitrary algebra, we provide generating function, Binet-style formula, Catalan-style identity, and d’Ocagne-type identity.

Suggested Citation

  • Flaut, Cristina & Shpakivskyi, Vitalii & Vlad, Elena, 2017. "Some remarks regarding h(x) – Fibonacci polynomials in an arbitrary algebra," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 32-35.
    • Handle: RePEc:eee:chsofr:v:99:y:2017:i:c:p:32-35
    DOI: 10.1016/j.chaos.2017.03.040
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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. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    3. Falcón, Sergio & Plaza, Ángel, 2009. "On k-Fibonacci sequences and polynomials and their derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1005-1019.
    4. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
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    Cited by:

    1. Eva Trojovská & Pavel Trojovský, 2021. "On Fibonacci Numbers of Order r Which Are Expressible as Sum of Consecutive Factorial Numbers," Mathematics, MDPI, vol. 9(9), pages 1-9, April.

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