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Hyperbolic \(\pmb k\)-Jacobsthal and \(\pmb k\)-Jacobsthal-Lucas Quaternions

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Abstract

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

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Acknowledgements

We thank the referee and the editor for all their comments and suggestions to improve the presentation.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Erzincan Binali Yıldırım University, Erzincan, Turkey

    Engin Özkan

  2. Graduate School of Natural and Applied Sciences, Erzincan Binali Yıldırım University, Erzincan, Turkey

    Mine Uysal

  3. Department of Mathematics, V. P. College Vaijapur, Vaijapur, Maharashtra, India

    A. D. Godase

Authors
  1. Engin Özkan
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  2. Mine Uysal
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  3. A. D. Godase
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Correspondence to Engin Özkan.

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Authors’ contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Mine UYSAL, Engin ÖZKAN and Ashok Dnyandeo GODASE. The first draft of the manuscript was written by Engin ÖZKAN and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.

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Özkan, E., Uysal, M. & Godase, A.D. Hyperbolic \(\pmb k\)-Jacobsthal and \(\pmb k\)-Jacobsthal-Lucas Quaternions. Indian J Pure Appl Math 53, 956–967 (2022). https://doi.org/10.1007/s13226-021-00202-9

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  • DOI: https://doi.org/10.1007/s13226-021-00202-9

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