Tables of the inverse Laplace transform of the function e -S-Beta

Abstract

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. We present here tables, accurate to six figures, of () for a number of values of between 0.25 and 0.999. In addition, since (), regarded as a function of , is uni-modal with a peak occurring at = we both tabulate and graph and 1/() as a function of , as well as giving polynomial approximations to 1/().