A brief survey of the study of power series and analytic functions on the Levi-Civita fields

摘要

In this survey paper, we will review the convergence and analytical properties of power series on the Levi-Civita field R (resp. C := E?iR) as well as the properties of the so-called R-analytic functions on an interval [a, b] of R. In particular, we will show that these have the same smoothness properties as real (resp. complex) power series and real analytic functions on an interval of R, respectively.