Aiming for the circuit characteristics of the Oldham RC fractal chain, the analytical expressions of Oldham RC fractal chain impedance function are deduced by using three methods at given initial impedances. Then, the solution methods are compared and analyzed. According to the continued fractional representation of the approximation circuit of Oldham fractal chain fractance, and the three-term recurrence formula of continuous fraction, a new mathematical representation of impedance function is introduced: continuous fractional three-term recursion matrix. By analyzing the Liu-Kaplan scaling iteration circuit and the scaling equations, two mathematical representations of the impedance functions of Liu-Kaplan fractal chains are deduced. Theoretical and experimental simulations compare the impedance function expressions and frequency characteristics of different fractional orders.