  We generalize the representation formula from slice-domains of regularity to
general Riemann slice-domains. This result allows us to extend the $*$-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.
