title: Exact and explicit probability densities for one-sided Lévy stable distributions.
abstract: We study functions gα(x) which are one-sided, heavy-tailed Lévy stable probability distributions of index α, 0<α<1, of fundamental importance in random systems, for anomalous diffusion and fractional kinetics. We furnish exact and explicit expressions for gα(x), 0 ≤ x<∞, for all α=l/k<1, with k and l positive integers. We reproduce all the known results given by k ≤ 4 and present many new exact solutions for k > 4, all expressed in terms of known functions. This will allow a "fine-tuning" of α in order to adapt gα(x) to a given experimental situation.
authors.affiliation: Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Université Pierre et Marie Curie, CNRS UMR 7600, Tour 13-5ième étage, Boîte Courrier 121, 4 place Jussieu, F 75252 Paris Cedex 05, France. penson@lptl.jussieu.fr
authors.forename: K A
authors.initials: KA
authors.lastname: Penson
authors.forename: K
authors.initials: K
authors.lastname: Górska