Fourier Transform
To describe results from spectroscopy or inelastic scattering, the sine or cosine Fourier transform of the stretched exponential is needed. It must be calculated either by numeric integration, or from a series expansion. The series here as well as the one for the distribution function are special cases of the Fox-Wright function. For practical purposes, the Fourier transform may be approximated by the Havriliak-Negami function, though nowadays the numeric computation can be done so efficiently that there is no longer any reason not to use the Kohlrausch-Williams-Watts function in the frequency domain.
Read more about this topic: Stretched Exponential Function
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