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Algorithms 2012, 5(4), 604-628; doi:10.3390/a5040604

Laplace–Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation “libkww”

Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science at FRM II, Lichtenbergstraße 1, 85747 Garching, Germany
Received: 12 October 2012 / Revised: 13 November 2012 / Accepted: 14 November 2012 / Published: 22 November 2012
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Abstract

The C library 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 ) for exponents β between 0.1 and 1.9 with double precision. 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 primitive of the cosine transform needed for the convolution integrals is also implemented. The software is hosted at http://apps.jcns.fz-juelich.de/kww; version 3.0 is deposited as supplementary material to this article.
Keywords: stretched exponential; Laplace–Fourier transform; numeric integration stretched exponential; Laplace–Fourier transform; numeric integration
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Wuttke, J. Laplace–Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation “libkww”. Algorithms 2012, 5, 604-628.

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