Abstract
In this article, we obtain an explicit expression of the difference and sum of the unit base in the Clifford analysis case by using the analogy with the complex one. These formulae then lead to the introduction of a class of Bernoulli polynomials in the Clifford analysis setting which are linked to the sum base. The newly introduced Bernoulli polynomials have properties which are very similar to those of the classical ones. Then we prove that each of the sum and difference of the unit base is of order 1. Finally, certain convergence properties of the difference and sum of simple monic bases of special monogenic polynomials are investigated. The obtained results generalize the complex case proved by Mikhail and Nassif to the Clifford setting.