I have a general formula of $$D = P_0 + \epsilon_1 E + \epsilon_2 E^2 + \epsilon_3 E^3 + ...$$
with $D$ as the electrical displacement, $E$ the electrical field, $P_0$ for the polarization at zero-field and $\epsilon$ the permittivity -> Source
With $E(t) = E cos(\omega t)$,
$$ D(t) = P_0 + \epsilon_1^*E_0 cos(wt) + \epsilon_2^*E_0^2 cos(2wt) + \epsilon_3^*E_0^3 cos(3wt)+ ...$$
and $D = \epsilon E$,
How do I go from: $$ D(t) = D_0 + D_1cos(wt) + D_2cos(2wt) + D_3cos(3wt)+ ...$$ to $$ D_0^* = P_0 + \frac{1}{2}\epsilon_2^*E_0^2 + \frac{3}{8}\epsilon_4^*E_0^4 + ... $$ $$ D_1^* = \epsilon_1^*E_0 + \frac{3}{4}\epsilon_3^*E_0^3 + \frac{10}{16}\epsilon_5^*E_0^5... $$ $$ D_2^* = \frac{1}{2}\epsilon_2^*E_0^2 + \frac{1}{2}\epsilon_4^*E_0^4 + \frac{15}{32}\epsilon_6^*E_0^6... $$ $$ D_3^* = \frac{1}{4}\epsilon_3^*E_0^3 + \frac{5}{16}\epsilon_5^*E_0^5 + \frac{21}{64}\epsilon_7^*E_0^7... $$
I'm pretty sure it has something to do with Fourier Transformation/Series but I'm not sure how to derive them.