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Dual-complex generalized k-Horadam numbers

The purpose of this paper is to provide a broad overview of the generalization of the various dual−complex number sequences, especially in the disciplines of mathematics and physics. By the help of dual numbers and dual−complex numbers, in this paper, we define the dual−complex generalized k−Horadam numbers. Furthermore, we investigate the Binet formula, generating function, some conjugation identities, summation formula and a theorem which is generalization of the Catalan’s identity, Cassini’s identity and d’Ocagne’s identity.