Fourier transform of the stretched exponential function: analytic error bounds, double exponential transform, and open-source implementation libkww. 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 articl
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References in zbMATH (referenced in 4 articles , 1 standard article )
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- Papamoschou, Dimitri: Modelling of noise reduction in complex multistream jets (2018)
- Silva, Fernando S.; Moreira, Davidson M.; Moret, Marcelo A.: Conformable Laplace transform of fractional differential equations (2018)
- Wuttke, Joachim: Laplace-Fourier transform of the stretched exponential function: analytic error bounds, double exponential transform, and open-source implementation “libkww” (2012)