On a new type of estimates of the accuracy of approximations in the CLT

The history of investigations accuracy of approximation in the central limit theorem has more seven decades, during which various estimates closeness of the distributions of sums of independent random variables to the normal distribution were obtained. The main drawback of these estimates is that they are very rough (although some of them impossible to improve). The report will be discussed on how to using selection the broad classes of distributions, changes the statement of problems and with involvement asymptotic expansions may be obtained estimates that many times more accurately known estimates.