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On Bi-periodic Jacobsthal and Jacobsthal-Lucas Quaternions

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  • Kubra Gul

Abstract

In this paper, we introduce the bi-periodic Jacobsthal and Jacobsthal-Lucas quaternions. We give the Binet formulas and the generating functions for these quaternions. We obtain some well-known identities such as the Cassini, Catalan and D’ocagne’s identities. Additionally, we give summation formulas and the relationships between bi-periodic Jacobsthal and Jacobsthal-Lucas quaternions.

Suggested Citation

  • Kubra Gul, 2019. "On Bi-periodic Jacobsthal and Jacobsthal-Lucas Quaternions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(2), pages 44-52, April.
    • Handle: RePEc:ibn:jmrjnl:v:11:y:2019:i:2:p:44
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    References listed on IDEAS

    as
    1. El Naschie, M.S., 2007. "The Fibonacci code behind super strings and P-Branes. An answer to M. Kaku’s fundamental question," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 537-547.
    2. Naschie, M.S.El, 2005. "Deriving the essential features of the standard model from the general theory of relativity," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 941-946.
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    More about this item

    Keywords

    Jacobsthal sequence; Jacobsthal-Lucas sequence; generalized Jacobsthal sequence; quaternion;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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