Special functions in Clifford analysis and axial symmetry

Abstract

In our previous paper ( Rend. Circ. Mat. Palermo 6 (1984), 259–269, we proved a general Laurent expansion for monogenic functions in symmetric domains of R m + 1 , depending on the kind of symmetry involved. In this paper we consider axial symmetric domains and we apply our results in order to introduce new special monogenic functions. We investigated axial exponential functions, generalized powerfunctions and generalized Hermite polynomials.