0911.4796 (Joachim Wuttke)

Fourier Transform of the Stretched Exponential Function: Analytic Error
Estimates, Double Exponential Transform, and Open-Source Implementation
libkww    [PDF]

Joachim Wuttke

An algorithm is described for computing the Laplace transform (one-sided Fourier sine and cosine transform) of the stretched (or compressed) exponential function exp(-t^beta) (also known as Kohlrausch-Williams-Watts function, as characteristic function of a Levy stable distribution, or as complementary cumulative Weibull distribution) for exponents beta between 0.1 and 2. For low and high frequencies, the well-known series expansions are used; for intermediate frequencies, the explicit integration is strongly accelerated by the Ooura-Mori double exponential transformation. The algorithm is implemented in C as library libkww. The source code is available at http://joachimwuttke.de/kww

View original: http://arxiv.org/abs/0911.4796