Cole–Davidson equation
The Cole-Davidson equation is a model used to describe dielectric relaxation in glass-forming liquids. The equation for the complex permittivity is where formula_2 is the permittivity at the high frequency limit, formula_3 where formula_4 is the static, low frequency permittivity, and formula_5 is the characteristic relaxation time of the medium. The exponent formula_6 represents the exponent of the decay of the high frequency wing of the imaginary part, formula_7. The Cole–Davidson equation is a generalization of the Debye relaxation keeping the initial increase of the low frequency wing of the imaginary part, formula_8. Because  this is also a characteristic feature of the Fourier transform of the stretched exponential function it has been considered as an approximation of the latter, although nowadays an approximation by the Havriliak-Negami function or exact numerical calculation may be preferred. Because the slopes of the peak in formula_9 in double-logarithmic representation are different it is considered an asymmetric generalization in contrast to the Cole-Cole equation. The Cole–Davidson equation is the special case of the Havriliak-Negami relaxation with formula_10. The real and imaginary parts are and