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Lévy stable two-sided distributions: Exact and explicit densities for asymmetric case

Lévy stable two-sided distributions: Exact and explicit densities for asymmetric case

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 asymmetry parameter beta: alpha = l/k and beta = (l - 2r)/k, where l, k and r are positive integers such that 0 < l/k …