On dual hyperbolic numbers with generalized Jacobsthal numbers components

Yüksel Soykan (), Erkan Taşdemir () and İnci Okumuş ()
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Yüksel Soykan: Zonguldak Bülent Ecevit University
Erkan Taşdemir: Kırklareli University
İnci Okumuş: İstanbul University-Cerrahpaşa

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 3, 824-840

Abstract: 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.

Keywords: Jacobsthal numbers; Jacobsthal-Lucas numbers; Dual hyperbolic numbers; Dual hyperbolic Jacobsthal numbers; Cassini identity; 11B39; 11B83 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00301-1

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