Some properties and identities of hyperbolic generalized k-Horadam quaternions and octonions

Document Type : Original paper

Authors

1 Department of Mathematics, Central University of Jharkhand, 835205, India

2 Department of Mathematics, Zonguldak Bülent Ecevit University, 67100, Turkey

Abstract

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.

Keywords

Main Subjects

References

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Communications in Combinatorics and Optimization
Volume 9, Issue 4
December 2024
Pages 707-724

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