Dual-complex generalızed k-horadam numbers

Abstract

The purpose of this paper is to provide a broad overview of thegeneralization of the various dual-complex number sequences, especially inthe 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 atheorem which is generalization of the Catalanís identity, Cassiniís identityand d'Ocagneís identity.