On the Rate of Convergence in the Central Limit Theorem

Let F_n(x) denote the distribution of the normalized partial sum of independent random variables with finite second moment, and write △_n(x)= |F_n(x)-Φ(x)|, whereΦ(x) is the standard normal distribution. In this paper, convergence rates in the central limit theorem are given, that is, under some conditions, we have 〓^^∞__ σ_n^2sn^∥〓_n(x)∥p<∞, where σ_n^2 is a variance of random variable and s_n^2 is a partial sum of variances