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Althoug Chebyshev  and Edeworth  had conceived of the formal expansions for distribution of sums of independent random variables, but only in Cramer's work  was laid a proper foundation of this problem. In the case when random variables are lattice Esseen get the asymptotic expansion in a new different form. Here we extend this problem for quasi-lattice random variables.doi:10.15388/lmr.2011.tt03 fatcat:2dotdfbn5zfghhi5lo7ledmdzm