On fourth-order jacobsthal quaternions

Authors : Gamaliel CERDA-MORALES

Pages : 73-79

Doi:10.33187/jmsm.434543

View : 12 | Download : 5

Publication Date : 2018-09-30

Article Type : Research Paper

Abstract :In this paper, we present for the first time a sequence of quaternions of order 4 that we will call the fourth-order Jacobsthal and the fourth-order Jacobsthal-Lucas quaternions. In particular, we are interested in the generating function, Binet formula, explicit formula and some interesting results for fourth-order Jacobsthal quaternions and fourth-order Jacobsthal-Lucas quaternions. This generalizes some previous results given by Szynal-Liana and Wloch in [13], Torunbalci Aydin and Yüce in [14] and Cerda-Morales in [2].
Keywords : Fourth order Jacobsthal number, Jacobsthal number, quaternion, Recurrence relation