Geodesic
Integral equations for equilibrium distribution functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 21 (1974) no. 1, pp. 146-152

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By explicit separation of the contribution of one, two,..., $s$ particles to the total potential energy of $N$ particles, a large number of systems of integral equations are obtained for the equilibrium distribution functions of simple liquids and gases, including as a special case the Kirkwood–Salzburg and Mayer–MontrolI systems of equations. Differentiation of the resulting equations with respect to the coordinate of any particle always leads to the BBGKY system. 
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     author = {N. K. Bolotin and Yu. P. Yudkin},
     title = {Integral equations for equilibrium distribution functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {21},
     number = {1},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1974_21_1_a13/}
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N. K. Bolotin; Yu. P. Yudkin. Integral equations for equilibrium distribution functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 21 (1974) no. 1, pp. 146-152. http://geodesic.mathdoc.fr/item/TMF_1974_21_1_a13/