Geodesic
The explicit formula of the Hilbert symbol for Honda formal groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 7, Tome 272 (2000), pp. 86-128

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In the present paper, we give an explicit formula for the Hilbert symbol in the case of Honda formal groups. The proof uses the Shafarevich basis and the relationship between the Lubin–Tate formal groups and Honda formal groups. 
@article{ZNSL_2000_272_a4,
     author = {S. V. Vostokov and O. V. Demchenko},
     title = {The explicit formula of the {Hilbert} symbol for {Honda} formal groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {86--128},
     publisher = {mathdoc},
     volume = {272},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_272_a4/}
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S. V. Vostokov; O. V. Demchenko. The explicit formula of the Hilbert symbol for Honda formal groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 7, Tome 272 (2000), pp. 86-128. http://geodesic.mathdoc.fr/item/ZNSL_2000_272_a4/