Analytical representations for relaxation functions of glasses

Analytical representations in the time and frequency domains are derived for the most frequently used phenomenological fit functions for non-Debye relaxation processes. In the time domain the relaxation functions corresponding to the complex frequency dependent Cole–Cole, Cole–Davidson and Havriliak–Negami susceptibilities are also represented in terms of H-functions. In the frequency domain the complex frequency dependent susceptibility function corresponding to the time dependent stretched exponential relaxation function is given in terms of H-functions. The new representations are useful for fitting to experiment.