Slice monogenic functions

Abstract. In this paper we offer a new definition of monogenicity for functions defined on R^{n+1} with values in the Clifford algebra R_n following an idea inspired by a recent paper by Gentili and Struppa. This new class of monogenic functions contains the polynomials (and, more in general, power series) with coefficients in the Clifford algebra R_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