, Volume 171, Issue 1, pp 385-403
Date: 10 Jul 2009

Slice monogenic functions

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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 the recent papers [6], [7]. 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.