Tables of the Inverse Laplace Transform of the Function [Formula: see text].

The inverse transform, [Formula: see text], 0 < < 1, is a stable law that arises in a number of different applications in chemical physics, polymer physics, solid-state physics, and applied mathematics. Because of its important applications, a number of investigators have suggested approximations to (). However, there have so far been no accurately calculated values available for checking or other purposes.

Stable Law Densities and Linear Relaxation Phenomena.

Stable law distributions occur in the description of the linear dielectric behavior of polymers, the motion of carriers in semi-conductors, the statistical behavior of neurons, and many other phenomena. No accurate tables of these distributions or algorithms for estimating the parameters in these relaxation models exist. In this paper we present tables of the functions together with related functional properties of ().