Description: In this paper, we show new representations of one-sided Levy stable distributions for irrational Levy indices of the type (p/q)^(l2/l1) which are not covered in [8] : for rational Levy indices. Furthermore, other equivalent representations for a distribution of a rational Levy index is described. We also give a simplest proof for the formulae which cover the cases for rational Levy indices. Finally we introduce the concepts of Levy smashing and Levy-smashed gamma stochastic processes.
The full-text article has been published in the "IntellectualArchive" journal , Vol.1, Num.3, July 2012, ISSN 1929-4700.