On ̄h-Jacobsthal and ̄h-Jacobsthal–Lucas sequences, and related quaternions

Abstract

In this paper, inspired by recent articles of A. Szynal-Liana & I. Włoch and F. T. Aydin & S. Yüce (see [26] and [2]), we will introduce the ̄h-Jacobsthal quaternions and the ̄h-Jacobsthal–Lucas sequences and their associated quaternions. The new results that we have obtained extend most of those obtained in [26].

Jacobsthal Representation Hybrinomials

“…[3,10,12]. In the literature we can find generalized Jacobsthal sequences which were used in studing hypercomplex numbers, see for example [1].…”