I have this adorable expression
$$\left(R_1+i\ \omega\ (L_1+L_2)-i\frac{1}{\omega\ C_1}\right)+\left( \frac{1}{-i\frac{1}{\omega\ C_2}}+\frac{1}{R_3+R_{Gap}+i\ \omega\ L_3} \right)^{-1},$$
with $R_{Gap}$ being the only unknown, and I'd like to map it to the form
$$R_x+i\ \left(\omega\ L_x-\frac{1}{\omega\ C_x}\right)+R_{Gap}.$$
This is a linearization for an impedance of a circuit with parallel elements.
Does somebody know how to make a series expansion of this, elucidating the situation with respect to $R_{Gap}$? I'd like to know the condition for the higher orders $R_{Gap}^n$ to not be relevant anymore w.r.t the main term. There will be some $(a+i\ b)\cdot R_{Gap}$ terms, which I guess I have to accept.
More on the motivation and the values of the constants, which might be relevant, are stated in this question:
https://physics.stackexchange.com/questions/65892/fitting-a-circuit-scheme-to-a-simpler-model