It is given by the equation
The exponent parameter , which takes a value between 0 and 1, allows to describe different spectral shapes. When , the Cole-Cole model reduces to the Debye model. When , the relaxation is stretched, i.e. it extends over a wider range on a logarithmic scale than Debye relaxation.
Cole-Cole relaxation constitutes a special case of Havriliak-Negami relaxation when the symmetry parameter (β) is equal to 1 - that is, when the relaxation peaks are symmetric. Another special case of Havriliak-Negami relaxation (β<1, α=0) is known as Cole-Davidson relaxation, for an abridged and updated review of anomalous dielectric relaxation in dissored systems see Kalmykov.
Cole, K.S.; Cole, R.H. (1942). "Dispersion and Absorption in Dielectrics - II Direct Current Characteristics". Journal of Chemical Physics. 10: 98–105. Bibcode:1942JChPh..10...98C. doi:10.1063/1.1723677.
Kalmykov, Y.P.; Coffey, W.T.; Crothers, D.S.F.; Titov, S.V. (2004). "Microscopic Models for Dielectric Relaxation in Disordered Systems". Physical Review E. 70: 041103. Bibcode:2004PhRvE..70d1103K. doi:10.1103/PhysRevE.70.041103.