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New families of Fibonacci and Lucas octonions with $$Q-$$ Q - integer components

Author

Listed:
  • Can Kızılateş

    (Zonguldak Bülent Ecevit University)

  • Emrah Polatlı

    (Zonguldak Bülent Ecevit University)

Abstract

A number of families of quaternion and octonion number sequence such as (Fibonacci quaternion, Fibonacci octonion and so forth) have been studied by several authors in many different ways. Besides, several formulas and identities involving these number sequences have been presented. The aim of this paper is to consider the octonions with components including quantum integers. We called these type of octonions the $$q-$$ q - Fibonacci octonions and the $$q-$$ q - Lucas octonions respectively. Furthermore, we give Binet formulas, exponential generating functions, summation formulas, Catalan identities, Cassini identities and d’Ocagne identities, respectively.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:1:d:10.1007_s13226-021-00073-0
    DOI: 10.1007/s13226-021-00073-0
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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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