Noncommutative Cauchy integral formula

Abstract

The aim of this paper is to provide and prove the most general Cauchy integral formula for slice regular functions and for C^1 functions on a real alternative *-algebra. Slice regular functions represent a generalization of the classical concept of holomorphic function of a complex variable in the noncommutative and nonassociative settings. As an application, we obtain two kinds of local series expansion for slice regular functions.Comment: 13 pages, an example has been added at the end of Section 4. To appear in "Complex Analysis and Operator Theory