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

The inverse transform, g(/) = Jf ~'(e~'^), 0<;3<1, is a stable law that arises in a number of different applications in chemical physics, polymer physics, solid-state pliysics, and applied mathematics. Because of its important applications, a number of investigators have suggested approximations to g{t). 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 g{t) for a number of values of fi between 0.25 and 0.999. In addition, since g{t), regarded as a function of /8, is unimodal with a peak occurring at t = tn^" we both tabulate and graph fmai and l/5('max) as a function of /3, as well as giving polynomial approximations to 1/