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On Representation of Densities of Stable Laws by Special Functions

A representation of the density of a one-dimensional strongly stable law via Meijer’s G-functions is obtained. The paper also considers the expressions of integral transforms with Euler kernels of these densities in terms of G-functions which make it possible to obtain representations of distribution functions of strongly stable laws with rational parameters. Some examples are given of representations of densities of multivariate spherically symmetric stable laws in terms of Meijer functions.