A local representation formula for quaternionic slice regular functions

After their introduction in 2006, quaternionic slice regular functions have mostly been studied over domains that are symmetric with respect to the real axis. This choice was motivated by some foundational results published 2009, such as Representation Formula for axially domains. The present work studies not symmetric, partly correcting hypotheses of previously results. In particular, this includes a Local valid without symmetry hypothesis. Moreover, it determines class domains, called simple, having following property: every function on simple domain can be uniquely extended completion its domain.