In recent years special hypercomplex Appell polynomials
have been introduced by several authors and their main properties
have been studied by different methods and with different
objectives. Like in the classical theory of Appell polynomials, the
generating function of hypercomplex Appell polynomials is a
hypercomplex exponential function. The observation that this
generalized exponential function has, for example, a close
relationship with Bessel functions confirmed the practical
significance of investigation on special classes of hypercomplex
differentiable functions. Its usefulness for combinatorial studies
has also been investigated. Moreover, an extension of those ideas
led to the construction of complete sets of hypercomplex Appell
polynomial sequences. Here we show how this opens the way for a more
systematic study of the relation between some classes of Special
Functions and Elementary Functions in Hypercomplex Function Theory.FC