Geodesic
The Hilbert symbol in multidimensional local fields for Lubin--Tate formal groups.~2
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 24, Tome 413 (2013), pp. 26-44

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In this paper an explicit formula for the Hilbert pairing between the Milnor $K$-group of multidimensional local field and the multidimensional Lubin–Tate formal module is derived. This formula is a generalization of such formula in one-dimensional case. Here we consider the case of characteristic $p>0$ of penultimate residue field. 
@article{ZNSL_2013_413_a1,
     author = {S. S. Afanas'eva},
     title = {The {Hilbert} symbol in multidimensional local fields for {Lubin--Tate} formal groups.~2},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {26--44},
     publisher = {mathdoc},
     volume = {413},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_413_a1/}
}
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S. S. Afanas'eva. The Hilbert symbol in multidimensional local fields for Lubin--Tate formal groups.~2. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 24, Tome 413 (2013), pp. 26-44. http://geodesic.mathdoc.fr/item/ZNSL_2013_413_a1/