Geodesic
The Hilbert symbol for Lubin--Tate formal groups.~I
Zapiski Nauchnykh Seminarov POMI, Modules and algebraic groups, Tome 114 (1982), pp. 77-95

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For the Hilbert Symbol on the group of points of a Lubin–Tate formal group there is found a modification of the explicit formulas that covers both the cases of an even and an odd prime $p$. 
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     author = {S. V. Vostokov},
     title = {The {Hilbert} symbol for {Lubin--Tate} formal {groups.~I}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {77--95},
     publisher = {mathdoc},
     volume = {114},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_114_a7/}
}
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S. V. Vostokov. The Hilbert symbol for Lubin--Tate formal groups.~I. Zapiski Nauchnykh Seminarov POMI, Modules and algebraic groups, Tome 114 (1982), pp. 77-95. http://geodesic.mathdoc.fr/item/ZNSL_1982_114_a7/