Table I.

The computed correlation functions were fitted with the corresponding fit function f(t) In the top part of the table the corresponding ${ℒ}_{DD}(\omega ),{ℒ}_{DJ}(\omega )$ and ${ℒ}_{JJ}(\omega )$ are used to calculate $ℒ\left[-\frac{d}{dt}{\text{Φ}}_D(t)\right]$ and $ℒ\left[-\frac{d}{dt}{\text{Φ}}_J(t)\right]$ by means of Eq. (9) and (15). At the bottom of the table $ℒ\left[-\frac{d}{dt}{\text{Φ}}_D(t)\right]$ is calculated directly.

correlation function	fit function f(t)	$ℒ[f(t)]$
〈MD(0) · MD(t)〉	${\displaystyle \sum _k{A}_k\cdot e^{-t/{\tau }_k}}$	${\displaystyle \sum _k\frac{A_k\cdot {\tau }_k}{1-i\omega {\tau }_k}}$	(Debye)	→ $\to {ℒ}_{DD}(\omega )$
〈MD(0) · J(t)〉	${\displaystyle \sum _k{A}_k{t}^{{\gamma }_k-1}\cdot e^{-t/{\tau }_k}}$	${\displaystyle \sum _k\frac{{\tilde{A}}_k}{{\left(1-i\omega {\tau }_k\right)}^{{\gamma }_k}}}$	(Cole - Davidson)	→ $\to {ℒ}_{DJ}(\omega )$
〈JD(0) · J(t)〉	${\displaystyle \sum _k{A}_k\cos \left({\omega }_k\cdot t+{\delta }_k\right)e^{-t/{\tau }_k}}$	${\displaystyle \sum _k\frac{A_k\cdot {\tau }_k\left(\cos \left({\delta }_k\right)\cdot \left(1-i\omega {\tau }_k\right)-{\omega }_k{\tau }_k\sin \left({\delta }_k\right)\right)}{{\tau }_k^2{\omega }_k^2+{\left(1-i\omega {\tau }_k\right)}^2}}$		→ $\to {ℒ}_{JJ}(\omega )$
correlation function	fit function f(t)	$ℒ\left[-\frac{d}{dt}f(t)\right]$
〈MD(0) · MD(t)〉	A ·e-(t/τ)β	$\frac{A}{{\left(1-{\left(i\omega {\tau }^{hn}\right)}^{{\alpha }^{hn}}\right)}^{{\gamma }^{hn}}}$	(Havriliak-Negami)