The main objective of this article is to consider complete orthonormal systems of monogenic polynomials together with their hypercomplex derivatives. Desired is that the derivatives of the basis polynomials are again basis functions from the original system. Based on this result, we prove an orthogonal decomposition of the space of square integrable monogenic functions with respect to the derivatives of arbitrary order.

We construct a family of hypercomplex Appell polynomials and it corresponding generating function of exponential type. An extension of this approach leads to the construction of a complete set of monogenic Appell polynomials. Moreover, it is shown how the obtained Appell family is connected with complete sets of solutions of the Riesz system.