The paper considers the problem of calculating the distribution function of a strictly stable law at $x\to\infty$. To solve this problem, an expansion of the distribution function in a power series was obtained, and an estimate of the remainder term was also obtained. It was shown that in the case $\alpha<1$ this series was convergent for any $x$, in the case $\alpha=1$ the series was convergent at $N\to\infty$ in the domain $|x|>1$, and in the case $\alpha>1$ the series was asymptotic at $x\to\infty$. The case $\alpha=1$ was considered separately and it was demonstrated that in that case the series converges to the generalized Cauchy distribution. An estimate for the threshold coordinate $x_\varepsilon^N$ was obtained which determined the area of applicability of the obtained expansion. It was shown that in the domain $|x|\geqslant x_\varepsilon^N$ this power series could be used to calculate the distribution function, which completely solved the problem of calculating the distribution function at large $x$.

翻译：本文研究了严格稳定律在$x\to\infty$时的分布函数计算问题。为解决该问题，得到了分布函数的幂级数展开式，并给出了余项估计。结果表明：当$\alpha<1$时，该级数对任意$x$均收敛；当$\alpha=1$时，级数在$N\to\infty$且$|x|>1$的区域内收敛；当$\alpha>1$时，级数在$x\to\infty$时呈渐近性。针对$\alpha=1$的情形进行了单独讨论，并证明此时级数收敛于广义柯西分布。本文给出了阈值坐标$x_\varepsilon^N$的估计，该坐标确定了所得展开式的适用区域。研究表明，在$|x|\geqslant x_\varepsilon^N$的区域内，该幂级数可用于计算分布函数，从而完全解决了大$x$值下分布函数的计算问题。