Some Properties and Identities of Hyperbolic Generalized k-Horadam Quaternions and Octonions.

The aim of this paper is to introduce the hyperbolic generalized k-Horadam quaternions and octonions and investigate their algebraic properties. We present some properties and identities of these quaternions and octonions for generalized k-Horadam numbers. Moreover, we give some determinants related to the hyperbolic generalized k-Horadam quaternions and octonions. Finally, we evaluate its determinants through the Chebyshev polynomials of the second kind and give an illustrative example as well. [ABSTRACT FROM AUTHOR]