In this paper, we have examined Cauchy products of central Delannoy numbers. Moreover, using their recurrence relation we have derived some important identities such as the Cassini and Catalan's identities which contain these products.

In the paper, we have considered the real and dual bicomplex numbers separately. Firstly, we examine the dual numbers and investigate the characteristic properties of them. Then, we give the definition, feature and related concepts about bicomplex numbers. And we define the number of dual k− Pell bicomplex numbers that are not found for the first time in the literature and we examine the norm and conjugate properties of these numbers. We give equations about conjugates and give also some important characteristic of these newly defined numbers, and we write the recursive correlations of these numbers. Using these relations we give some important identities such as Vajda's, Honsberger's and d'Ocagne identities.

No abstract