Mathematical functions for the analysis of luminescence decays with underlying distributions 1. Kohlrausch decay function (stretched exponential)

The Kohlrausch (stretched exponential) decay law is analyzed in detail. Analytical and approximate forms of the distribution of rate constants and related functions are obtained for this law. A simple generalization of the Kohlrausch decay law that eliminates unphysical aspects of the original form is introduced and fully characterized. General results concerning the relation between decay law and distribution of rate constants are also obtained.