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

The inverse transform, g ( t ) = L − 1 ( e − s β ) , 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 ).