The Hilbert symbol of a polynomial formal group

We constract an explicit formula for the analogue of Hilbert pairing over universal formal modules for polynomial formal group of integer ring of local field is constructed. This pairing is well-defined, invariant under the change of variables and has a property similar to the invariance under the change of series expansion. Aim of this construction is to obtain explicit formulae for generalised Hilbert pairing over arbitrary formal module for polynomial formal group of local ring.