Exact and explicit probability densities for one-sided Lévy stable distributions.

@article{Penson2010ExactAE,
  title={Exact and explicit probability densities for one-sided L{\'e}vy stable distributions.},
  author={K. Penson and K. G{\'o}rska},
  journal={Physical review letters},
  year={2010},
  volume={105 21},
  pages={
          210604
        }
}
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… Expand

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