Tables of the Inverse Laplace Transform of the Function [... formula ...]

The inverse transform, g(t) = ?^?1(e^?sβ), 0 < β < 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 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 β between 0.25 and 0.999. In addition, since g(t), regarded as a function of β, is uni-modal with a peak occurring at t = t_max we both tabulate and graph t_max and 1/g(t_max) as a function of β, as well as giving polynomial approximations to 1/g(t_max).