Wildly ramified power series with large multiplicity

In this paper we consider wildly ramified power series, i.e. , series defined over a field of positive characteristic, fixing the origin, where it is tangent to identity. setting introduce new invariant under change coordinates called second residue fixed point index and provide closed formula for it. As name suggests closely related index, they coincide in case that have small multiplicity. Finally, characterize with large multiplicity having smallest possible at origin iteration, terms invariant.