The calculation of the probability density of a strictly stable law at large X
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The article is devoted to the problem of calculating the probability density of a strictly stable law at x→∞. 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<α<1 and asymptotic at x→∞ in the case 1<α<2. The case α=1 was considered separately. It was shown that in the case α=1 the obtained power series was convergent for any |x|>1 at N→∞. It was also shown that in this case it was convergent to the density of g(x,1,θ). An estimate of the threshold coordinate x_ε^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|⩾ x_ε^N this power series could be used to calculate the probability density.
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