Tables of the Inverse Laplace Transform of the Function [Formula: see text].
The inverse transform, [Formula: see text], 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 tog(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, ofg(t) for a number of values ofβbetween 0.25 and 0.999. In addition, sinceg(t), regarded as a function ofβ, is uni-modal with a peak occurring att=tmaxwe both tabulate and graphtmaxand 1/g(tmax) as a function ofβ, as well as giving polynomial approximations to 1/g(tmax).
National Institute of Standards and Technology, Gaithersburg, MD 20899.
Menachem
M
Dishon
General Electric Corporate Research and Development, Schenectady, NY 12301.
John T
JT
Bendler
National Institutes of Health, Bethesda, MD 20892.
George H
GH
Weiss
numerical inversion of Laplace transforms; relaxation processes; stable laws; stretched exponentials