Riemann slice-domains over quaternions II

Abstract

We generalize the representation formula from slice-domains of regularity to general Riemann slice-domains. This result allows us to extend the $\ast$-product of slice regular functions on axially symmetric domains to certain Riemann slice-domains by introducing holomorphic stem systems and tensor holomorphic functions. In particular, we construct a power series expansions of slice regular functions on certain Riemann slice-domains, which implies a relation between stem holomorphic, tensor holomorphic and slice regular functions.

49 pages