The article is devoted to the problem of calculating the probability density of a strictly stable law at $x\to\infty$. To solve this problem, it was proposed to use the expansion of the probability density in a power series. A representation of the probability density in the form of a power series and an estimate for the remainder term was obtained. This power series is convergent in the case $0<\alpha<1$ and asymptotic at $x\to\infty$ in the case $1<\alpha<2$. The case $\alpha=1$ was considered separately. It was shown that in the case $\alpha=1$ the obtained power series was convergent for any $|x|>1$ at $N\to\infty$. It was also shown that in this case it was convergent to the density of $g(x,1,\theta)$. An estimate of the threshold coordinate $x_\varepsilon^N$, was obtained which determines the range of applicability of the resulting expansion of the probability density in a power series. It was shown that in the domain $|x|\geqslant x_\varepsilon^N$ this power series could be used to calculate the probability density.

翻译：本文致力于研究严格稳定律在$x\to\infty$时的概率密度计算问题。为解决该问题，提出了利用概率密度的幂级数展开方法。得到了概率密度的幂级数表示形式及其余项估计。该幂级数在$0<\alpha<1$情形下收敛，在$1<\alpha<2$情形下当$x\to\infty$时具有渐近性。单独讨论了$\alpha=1$的情形。结果表明，在$\alpha=1$情形下，当$N\to\infty$时，所得到的幂级数对任意$|x|>1$均收敛。同时证明，在此情形下该幂级数收敛于密度函数$g(x,1,\theta)$。得到了阈值坐标$x_\varepsilon^N$的估计，该估计确定了概率密度幂级数展开式的适用区间。研究表明，在$|x|\geqslant x_\varepsilon^N$区域内，该幂级数可用于计算概率密度。