Dual-hyperbolic Pell quaternions

Abstract

In this paper, dual-hyperbolic Pell numbers and Pell quaternions are defined. Also, some algebraic properties of dual-hyperbolic Pell numbers and quaternions which are connected with dual-hyperbolic numbers and Pell numbers are investigated. Furthermore, the Honsberger identity, the O'cagne's identity, the generating functions, Binet's formula, Cassini's identity, Catalan's identity for these quaternions are given.