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On higher order Fibonacci hyper complex numbers

Author

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  • Kızılateş, Can
  • Kone, Tiekoro

Abstract

This paper deals with developing a new class of quaternions, octonions and sedenions called higher order Fibonacci 2m-ions (or-higher order Fibonacci hyper complex numbers) whose components are higher order Fibonacci numbers. We give recurrence relation, Binet formula, generating function and exponential generating function of higher order Fibonacci 2m-ions. We also derive some identities such as Vajda’s identity, Catalan’s identity, Cassini’s identity, and d’Ocagne’s identity with the aid of the Binet formula. Finally, we develop some matrix identities involving higher order Fibonacci 2m-ions which allow us to obtain some properties of these higher order hyper complex numbers.

Suggested Citation

  • Kızılateş, Can & Kone, Tiekoro, 2021. "On higher order Fibonacci hyper complex numbers," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921003982
    DOI: 10.1016/j.chaos.2021.111044
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    Cited by:

    1. Nazlıhan Terzioğlu & Can Kızılateş & Wei-Shih Du, 2022. "New Properties and Identities for Fibonacci Finite Operator Quaternions," Mathematics, MDPI, vol. 10(10), pages 1-13, May.

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