Convergence on the Levi-Civita field and study of power series (Q2751743)

The intermediate value theorem for ``continuous'' functions on a closed interval of a non-archimedean field is in general false due to the disconnectedness of such fields in the order topology. In this paper the authors investigate the behavior of power series on the so-called Levi-Civita fields. In particular, their results show that the power series of the elementary functions exp, cos, sin, cosh, sinh converge absolutely in the weak sense of the Levi-Civita field. It is also shown that for the expandable functions, the intermediate value theorem holds.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00058].