The significance level and power of two-sided Kolmogorov's test in case of small sample sizes

Calculating $n$-dimensional ($1\le n<\infty$) integrals over a domain restricted by $(n+1)$-dimensional hyperplanes, we obtain a recurrent relation for the significance level $\beta_n$ and power $P_n$ of two-sided Kolmogorov's test which can be used to get exact values of $\beta_n$ and $P_n$ in case of small sample sizes.