Starting with the differential: representation of monogenic functions by polynomials of non-monogenic variables

This paper deals with different power series expansions of generalized holomorphic (monogenic) functions in the setting of Clifford Analysis. Our main concern are generalized Appell polynomials as a special class of monogenic polynomials which have been introduced in 2006 by two of the authors using several monogenic hypercomplex variables. We clarify the reasons why a particular pair of non-monogenic variables allows to obtain a power series expansion by those generalized Appell polynomials. The approach is based on the differential of a function. Some other monogenic polynomials as well as applications are mentioned.This work was supported by Portuguese funds through the CMAT - Research Centre of Mathematics of University of Minho - and through the CIDMA-Center of Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT -Fundação para a Ciência e Tecnologia”), within projects UIDB/00013/2020, UIDP/00013/2020, UIDB/04106/2020 and UIDP/04106/2020