Lubin–Tate series ($f(T)$)

For a uniformizer $\pi$ of a non-Archimedean local field $K$ with residue field of cardinality $q$, a Lubin–Tate series is a series $f(T)\in {\mathcal{O}}_K[[T]]$ satisfyingIt determines the associated two-variable Lubin–Tate formal group. A useful example is $f(T)=\pi T+T^q$. For $K={\mathbb{Q}}_p$ and $\pi =p$, the choice $(1+T{)}^p-1$ gives the formal multiplicative group and the Lubin–Tate cyclotomic example.