Geodesic
On asymptotic expansions for distribution functions of sums of independent random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 328-338

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Let $\{X_j\}$ be a sequence of independent identically distributed random variables with zero means and unit variances and let $F_n(x)$ be the distribution function of the sum $\frac1{\sqrt n}\sum_{j=1}^nX_j$. Asymptotic expansions of the function $F_n(x)$ are given which are more general than the classic expansion (0.1). We study also the asymptotic behaviour of the remainder in (0.1). 
@article{TVP_1971_16_2_a9,
     author = {L. V. Osipov},
     title = {On asymptotic expansions for distribution functions of sums of independent random variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {328--338},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a9/}
}
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L. V. Osipov. On asymptotic expansions for distribution functions of sums of independent random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 328-338. http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a9/