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On dual hyperbolic numbers with generalized Jacobsthal numbers components

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Abstract

In this paper, we introduce the generalized dual hyperbolic Jacobsthal numbers. As special cases, we deal with dual hyperbolic Jacobsthal and dual hyperbolic Jacobsthal-Lucas numbers. We present Binet’s formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan’s, Cassini’s, d’Ocagne’s, Gelin-Cesàro’s, Melham’s identities and present matrices related with these sequences.

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Authors and Affiliations

  1. Department of Mathematics Art and Science Faculty, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey

    Yüksel Soykan

  2. Pınarhisar Vocational School, Kırklareli University, 39300, Kırklareli, Turkey

    Erkan Taşdemir

  3. Department of Engineering, Faculty of Engineering, İstanbul University-Cerrahpaşa, 34100, İstanbul, Turkey

    İnci Okumuş

Authors
  1. Yüksel Soykan
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  2. Erkan Taşdemir
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  3. İnci Okumuş
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Correspondence to Erkan Taşdemir.

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Communicated by B. Sury.

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Soykan, Y., Taşdemir, E. & Okumuş, İ. On dual hyperbolic numbers with generalized Jacobsthal numbers components. Indian J Pure Appl Math 54, 824–840 (2023). https://doi.org/10.1007/s13226-022-00301-1

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  • DOI: https://doi.org/10.1007/s13226-022-00301-1

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