Dual-complex k-Pell quaternions

Abstract

In this paper, dual-complex k-Pell numbers and dual-complex k-Pell quaternions are defined. Also, some algebraic properties of dual-complex k-Pell numbers and quaternions which are connected with dual-complex numbers and k-Pell numbers are investigated. Furthermore, Honsberger Identity, d'Ocagne's Identity, Binet's Formula, Cassini's Identity and Catalan's Identity for these quaternions are given.