Kiister, G., On the Hurwitz product of formal power series and automata, Theoretical Computer Science 83 (1991) 261-273. The Hurwitz (shuffle) product defined on formal power series is generalized to matrices and therefore to automata. The resulting constructions are then used to study commutative power series and abstract families of power series. In particular, the families of power series re...

Abstract This article is a natural continuation of the paper Tiwari, D., Giordano, P., Hyperseries in non-Archimedean ring Colombeau generalized numbers this journal. We study one variable hyper-power series by analyzing notion radius convergence and proving classical results such as algebraic operations, composition reciprocal series. then define real analytic functions, considering their deri...