  Explicit descriptions of local integral Galois module generators in certain
extensions of $p$-adic fields due to Pickett have recently been used to make
progress with open questions on integral Galois module structure in wildly
ramified extensions of number fields. In parallel, Pulita has generalised the
theory of Dwork's power series to a set of power series with coefficients in
Lubin-Tate extensions of $\Q_p$ to establish a structure theorem for rank one
solvable p-adic differential equations.
  In this paper we first generalise Pulita's power series using the theories of
formal group exponentials and ramified Witt vectors. Using these results and
Lubin-Tate theory, we then generalise Pickett's constructions in order to give
an analytic representation of integral normal basis generators for the square
root of the inverse different in all abelian totally, weakly and wildly
ramified extensions of a p-adic field. Other applications are also exposed.
