## 1 Introduction
### Complex Dielectric Permittivity  
According to the expressions (A14a), (A14b), and (92), the total polarization of the dielectric is represented as  
\[\mathrm{P}^{(\Omega)}(\mathrm{t})=\sum_{\lambda=0}^{\infty}\hat{\alpha}_{2 \lambda}^{(\Omega_{2\lambda+1})}\cdot\mathrm{E}_{\mathrm{pol}}^{2\lambda+1}( \mathrm{t}). \tag{93}\]  
In (93), \(\hat{\alpha}_{2\lambda}^{(\Omega_{2\lambda+1})}\) is defined based on the set \(\Omega_{2\lambda+1}=\left\{\omega;2\omega;3\omega,\ldots,2\lambda\omega;(2 \lambda+1)\,\omega\right\}\), a complex function of parameters of relaxers and temperature \(\hat{\alpha}_{2\lambda}^{(\Omega_{2\lambda+1})}(\mathrm{U}_{0},\delta_{0}, \gamma_{0},n_{0},a;\mathrm{T})=\frac{\mathrm{P}^{((2\lambda+1)\omega)}(\mathrm{ t})}{\mathrm{E}_{\mathrm{pol}}^{2\lambda+1}(\mathrm{t})}\), indicating a component of the order of \(2\lambda\) from the polarization decomposition \(\mathrm{P}^{(\Omega)}(\mathrm{t})\) in a row by odd degrees of intensity of the polarizing field \(\mathrm{E}_{\mathrm{pol}}(\mathrm{t})\). Here, \(\lambda=\left\{0,1,2,3,\ldots\right\}\). Polarization at a frequency of \((2\lambda+1)\omega\) is calculated from the expression  
\[\mathrm{P}^{((2\lambda+1)\omega)}(\mathrm{t})=\frac{\mathrm{q}}{\mathrm{d}} \mathrm{\sum}_{\lambda=0}^{\infty}\int_{0}^{\mathrm{d}}\mathrm{x}\rho^{((2 \lambda+1)\omega)}(\xi,\tau)\mathrm{d}\mathrm{x},\] (93a) adjusted based on ( 88 ) to \[\mathrm{P}^{((2\lambda+1)\omega)}(\mathrm{t})=-\frac{2\mathrm{q}\mathrm{d}}{ \pi^{2}}\mathrm{\sum}_{\alpha=1k}^{\infty}\mathrm{\sum}_{-2\lambda+1}^{ \infty}\frac{\Re_{k}^{((2\lambda+1)\omega)}(\mathrm{n},\tau)}{\mathrm{n}^{2}} \times\sin^{2}\left(\frac{\pi n}{2}\right). \tag{93b}\]  
As shown, substituting recurrent formulas (72) and (83) into (93b) yields expressions (A14a) and (92). By comparing the formula \(\mathrm{P}^{(\Omega)}(\mathrm{t})=\hat{\alpha}^{(\Omega)}\cdot\mathrm{E}_{ \mathrm{pol}}(\mathrm{t})\) with expression (93), we express the complex dielectric susceptibility (CDS) in the form of decomposition in a row under even degrees of tension of the polarizing field \(\mathrm{E}_{\mathrm{pol}}(\mathrm{t})\):  
\[\hat{\alpha}^{(\Omega)}=\sum_{\lambda=0}^{\infty}\hat{\alpha}_{2\lambda}^{( \Omega_{2\lambda+1})}\cdot\mathrm{E}_{\mathrm{pol}}^{2\lambda}(\mathrm{t}). \tag{94}\]  
Based on (29) \(\hat{\alpha}_{2\lambda}^{(\Omega_{2\lambda+1})}\cdot\mathrm{E}_{\mathrm{pol} }^{2\lambda}(\mathrm{t})=\hat{\alpha}^{(\Omega_{2\lambda+1})}=\frac{\mathrm{P} ^{((2\lambda+1)\omega)}(\mathrm{t})}{\mathrm{E}_{\mathrm{pol}}(\mathrm{t})}\), we also have  
\[\hat{\alpha}^{(\Omega)}=\sum_{\lambda=0}^{\infty}\hat{\alpha}^{(\Omega_{2 +1})}. \tag{95}\]By assuming there is polarization in the form of \(\mathrm{P}^{(\Omega)}(\mathrm{t})=\epsilon_{0}\Big{(}\dot{\varepsilon}^{(\Omega)}- \varepsilon_{\infty}\Big{)}\mathrm{E}_{\mathrm{pol}}(\mathrm{t})\), we can find the complex dielectric permeability (CDP):  
\[\dot{\varepsilon}^{(\Omega)}=\varepsilon_{\infty}+\frac{\hat{\alpha}^{(\Omega) }}{\varepsilon_{0}}. \tag{96}\]  
Substituting (94) into (96) yields  
\[\dot{\varepsilon}^{(\Omega)}=\varepsilon_{\infty}+\sum_{\lambda=0}^{\infty} \hat{\varepsilon}_{2\lambda}^{(\Omega_{2\lambda+1})}\mathrm{E}_{\mathrm{pol} }^{2\lambda}(\mathrm{t}), \tag{97}\]  
\[\dot{\varepsilon}^{(\Omega)}=\varepsilon_{\infty}+\sum_{\lambda=0}^{\infty} \hat{\varepsilon}^{(\Omega_{2\lambda+1})}. \tag{98}\]  
Here, \(\hat{\varepsilon}_{2\lambda}^{(\Omega_{2\lambda+1})}=\frac{\hat{\alpha}_{2 \lambda+1}^{(\Omega_{2\lambda+1})}}{\varepsilon_{0}}\), \(\hat{\alpha}_{2\lambda}^{(\Omega_{2\lambda+1})}=\frac{\mathrm{P}^{(\Omega_{2 \lambda+1})}\mathrm{(t)}}{\mathrm{E}_{\mathrm{pol}}(\mathrm{t})}\), and \(\hat{\varepsilon}^{(\Omega_{2\lambda+1})}=\hat{\varepsilon}_{2\lambda}^{( \Omega_{2\lambda+1})}\cdot\mathrm{E}_{\mathrm{pol}}^{2\lambda}(\mathrm{t})\).