• Honam Mathematical Journal
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• v.46 no.4
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• pp.677-696
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• 2024

In this study, we introduce a new generalization of the Leonardo sequence, dual quaternions with the 𝓓𝓖𝓒 Leonardo sequence coefficients, depending on the parameter p ∈ ℝ. This generalization gives dual quaternions with the dual-complex Leonardo sequence for 𝖕 = -1, dual quaternions with the hyper-dual Leonardo sequence for 𝖕 = 0, and dual quaternions with the dual-hyperbolic Leonardo sequence for 𝖕 = 1. The basic algebraic structures and some special characteristic relations are presented, as well as the Binet's formula, generating function, d'Ocagne's, Catalan's, Cassini's, and Tagiuri's identities.