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Hyperbolic $$\pmb k$$ k -Jacobsthal and $$\pmb k$$ k -Jacobsthal-Lucas Quaternions

Author

Listed:
  • Engin Özkan

    (Erzincan Binali Yıldırım University)

  • Mine Uysal

    (Erzincan Binali Yıldırım University)

  • A. D. Godase

    (V. P. College Vaijapur)

Abstract

In this paper, we introduce the hyperbolic $$k-$$ k - Jacobsthal and $$k-$$ k - Jacobsthal-Lucas quaternions. We present generating functions, Binet formula, Catalan’s identity, Vajda’s identity etc. for the hyperbolic k-Jacobsthal and $$k-$$ k - Jacobsthal-Lucas quaternions.

Suggested Citation

  • Engin Özkan & Mine Uysal & A. D. Godase, 2022. "Hyperbolic $$\pmb k$$ k -Jacobsthal and $$\pmb k$$ k -Jacobsthal-Lucas Quaternions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 956-967, December.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:4:d:10.1007_s13226-021-00202-9
    DOI: 10.1007/s13226-021-00202-9
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    References listed on IDEAS

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    1. A. D. Godase, 2019. "Properties of k-Fibonacci and k-Lucas octonions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(4), pages 979-998, December.
    2. Çelik, Songül & Durukan, İnan & Özkan, Engin, 2021. "New recurrences on Pell numbers, Pell-Lucas numbers, Jacobsthal numbers, and Jacobsthal-Lucas numbers," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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