Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation libkww
Mathematical Physics
2012-11-26 v3 math.MP
Abstract
The C library \texttt{libkww} provides functions to compute the Kohlrausch-Williams-Watts function, i.e.\ the Laplace-Fourier transform of the stretched (or compressed) exponential function for exponents between 0.1 and 1.9 with sixteen-digits accuracy. Analytic error bounds are derived for the low and high frequency series expansions. For intermediate frequencies the numeric integration is enormously accelerated by using the Ooura-Mori double exponential transformation. The source code is available from the project home page \url{http://apps.jcns.fz-juelich.de/doku/sc/kww}.
Cite
@article{arxiv.0911.4796,
title = {Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation libkww},
author = {Joachim Wuttke},
journal= {arXiv preprint arXiv:0911.4796},
year = {2012}
}
Comments
Version 3. 11 pages, 4 figures. Describes software version 2.0