Geodesic
On the refinement of the remainder term in the central limit theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 3, pp. 688-691

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Some new estimates are given for the accuracy of approximation of the distribution functions $F_n$ of normalized sums of independent and identically distributed random variables by the standard normal distribution function $\Phi$. Various metrics are used (uniform, non-uniform with weight $1+x^2$, average metric and average metric with weight $|x|$). 
@article{TVP_1978_23_3_a24,
     author = {R. Z. Salahytdinov},
     title = {On the refinement of the remainder term in the central limit theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {688--691},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_3_a24/}
}
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R. Z. Salahytdinov. On the refinement of the remainder term in the central limit theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 3, pp. 688-691. http://geodesic.mathdoc.fr/item/TVP_1978_23_3_a24/