In this paper, we show new representations of one-sided L\'{e}vy stable
distributions for irrational L\'{e}vy indices of the type
(qp)l1l2 which are not covered in
\cite{pg1} : for rational L\'{e}vy indices. Furthermore, other equivalent
representations for a distribution of a rational L\'{e}vy index is described.
We also give a simplest proof for the formulae which cover the cases for
rational L\'{e}vy indices. Finally we introduce the concepts of L\'{e}vy
smashing and L\'{e}vy-smashed gamma stochastic processes.Comment: Welcome for comment