English

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 exp(tβ)\exp(-t^\beta) for exponents β\beta 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

R2 v1 2026-06-21T14:15:50.022Z