  In classical function theory, a function is holomorphic if and only if it is
complex analytic. For higher dimensional spaces it is natural to work in the
context of Clifford algebras. The structures of these algebras depend on the
parity of the dimension n of the underlying vector space. The theory of
holomorphic Cliffordian functions reflects this dependence. In the case of odd
n the space of functions is defined by an operator (the Cauchy-Riemann
equation) but not in the case of even $n$. For all dimensions the powers of
identity (z^n, x^n) are the foundation of function theory.
