Bicomplex generalized k-horadam quaternions

Abstract

This study provides a broad overview of the generalization of the various quaternions,especially in the context of its enhancing importance in the disciplines of mathematics and physics. By the help of bicomplex numbers, in this paper, we define the bicomplex generalized k-Horadam quaternions. Fundamental properties and mathematical preliminaries of these quaternions are outlined. Finally, we give some basic conjucation identities, generating function,the Binet formula, summation formula, matrix representation and a generalized identity, which is generalization of the well-known identities such as Catalan’s identity, Cassini’s identity and d’Ocagne’s identity, of the bicomplex generalized k-Horadam quaternions in detail.