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

The purpose of this paper is to combine the (q,q ')$$ \left(q,{q}^{\prime}\right) $$-calculus in the quaternionic context, which is proposed via two kinds of (q,q ')$$ \left(q,{q}^{\prime}\right) $$-operators, with the theory of slice regular functions. Specifically, we shall work in suitable subclasses of slice regular functions in which the (q,q ')$$ \left(q,{q}^{\prime}\right) $$-operators can be related with the slice derivative. The paper presents some results such as an integral formula and series expansion.