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We study the one-dimensional Levy stable density distributions g(alpha, beta;x) for -infty < x < infty, for rational values of index alpha and the asymmetryparameter beta: alpha = l/k and beta = (l - 2r)/k, where l, k and r arepositive integers such that 0 < l/k < 1 for 0 <= r <= l and 1 < l/k <= 2 forl-k <= r <= k. We treat both symmetric (beta = 0) and asymmetric (beta neq 0)cases. We furnish exact and explicit forms of g(alpha, beta; x) in terms ofknown functions for any admissible values of alpha and beta specified by atriple of integers k, l and r. We reproduce all the previously known exactresults and we study analytically and graphically many new examples. We pointout instances of experimental and statistical data that could be described byour solutions.

Levy stable two-sided distributions: exact and explicit densities for asymmetric case