  In this paper we offer a definition of monogenicity for functions defined on
$\rr^{n+1}$ with values in the Clifford algebra $\rr_n$ following an idea
inspired by the recent papers \cite{gs}, \cite{advances}. This new class of
monogenic functions contains the polynomials (and, more in general, power
series) with coefficients in the Clifford algebra $\rr_n$. We will prove a
Cauchy integral formula as well as some of its consequences. Finally, we deal
with the zeroes of some polynomials and power series.
