Dual-complex generalized k-Horadam numbers

Abstract

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 de…ne 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.

Fundamental properties of extended Horadam numbers

“…For the special real values p = −1, p = 0 and p = 1, dual-complex, hyper-dual, dual-hyperbolic, hyperbolic-complex, bihyperbolic and bicomplex numbers are obtained from DGC, HGC and CGC numbers (see detailed classification in [12]). As we move from number systems to elements of Horadam sequences, some papers can be examined in literature, [2,4,7,11,13,14,24,28,33].…”