An approach to slice regular functions via post‐quantum calculus theory

Abstract

The purpose of this paper is to combine the ‐calculus in the quaternionic context, which is proposed via two kinds of ‐operators, with the theory of slice regular functions. Specifically, we shall work in suitable subclasses of slice regular functions in which the ‐operators can be related with the slice derivative. The paper presents some results such as an integral formula and series expansion.