Geodesic
Local Limit Theorems for Non-Identical Lattice Distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 7 (1962) no. 3, pp. 344-346

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Asymptotic expansions are obtained in a local limit theorem for the sum of non-identically distributed independent random variables having lattice distributions with finite moments of integer order $k\geq3$. The theorem stated is a generalization of a result by Esseen. 
@article{TVP_1962_7_3_a8,
     author = {V. V. Petrov},
     title = {Local {Limit} {Theorems} for {Non-Identical} {Lattice} {Distributions}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {344--346},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {1962},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1962_7_3_a8/}
}
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V. V. Petrov. Local Limit Theorems for Non-Identical Lattice Distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 7 (1962) no. 3, pp. 344-346. http://geodesic.mathdoc.fr/item/TVP_1962_7_3_a8/