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

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

2009-11-25

arxiv.org/abs/0911.4796v1

Physics

Mathematical Physics

10 pages, 4 figures

Scientific paper

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://www.messen-und-deuten.de/kww

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