Recent experiments have shown that photoluminescence decay of silicon nanocrystals can be described by the stretched exponential function. We show here that the associated decay probability rate is the one-sided Levy stable distribution which describ
es well the experimental data. The relevance of these conclusions to the underlying stochastic processes is discussed in terms of Levy processes.
Symbolic methods of umbral nature play an important and increasing role in the theory of special functions and in related fields like combinatorics. We discuss an application of these methods to the theory of lacunary generating functions for the Lag
uerre polynomials for which we give a number of new closed form expressions. We present furthermore the different possibilities offered by the method we have developed, with particular emphasis on their link to a new family of special functions and with previous formulations, associated with the theory of quasi monomials.
