Bicomplex Third-order Jacobsthal Quaternions

Abstract

The aim of this work is to consider the bicomplex third-order Jacobsthal quaternions and to present some properties involving this sequence, including the Binet-style formulae and the generating functions. Furthermore, Cassini's identity and d'Ocagne's identity for this type of bicomplex quaternions are given, and a different way to find the $n$-th term of this sequence is stated using the determinant of a four-diagonal matrix whose entries are bicomplex third-order quaternions.

11 pages

References in corpus (3)

• On a Generalization for Tribonacci Quaternions
• Dual Third-order Jacobsthal Quaternions
• Third-order Jacobsthal Generalized Quaternions