On Some Q-Dual Bicomplex Jacobsthal Numbers

Abstract

In this study, we benefited from dual bicomplex numbers and quantum analysis studies, which were previously defined with the help of dual numbers. We defined Jacobsthal and Jacobsthal Lucas dual bicomplex number sequences whose coefficients are associated with q-integers. Then, we gave some basic properties of the newly defined number sequences and their relations with each other. We also derived the generating functions and Binet formulas for these sequences. In addition, using these formulas, we gave important identities such as Vajda, Honsberger and d’Ocagne identities which provide the elements of the defined sequences. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.