The calculation of the distribution function of a strictly stable law at large X
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The paper considers the problem of calculating the distribution function of a strictly stable law at x→∞. 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 α<1 this series was convergent for any x, in the case α=1 the series was convergent at N→∞ in the domain |x|>1, and in the case α>1 the series was asymptotic at x→∞. The case α=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_ε^N was obtained which determined the area of applicability of the obtained expansion. It was shown that in the domain |x|⩾ x_ε^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.
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