I am looking for the transfer function of three cascaded RC filters:

I have found the solution for two RC cascades (components differently labeled):

I need an analytical expression like this one for three cascaded RC stages, because I need to fit such a function to experimentally measured data from a network with unknown components Ri and Ci.

I tried to find the function myself using KCL and KVL but expressions tend to get awfully long and so far I didn't manage to find a transfer function that is in agreement with simulations of such networks.

Maybe one of you guys has the transfer function for three cascaded RC filters at hand? Or is there probably a different way to find the components Ri and Ci for a system like that from measured data Vout/Vi(frequency)?

I am looking for the transfer function of three cascaded RC filters:

I have found the solution for two RC cascades (components differently labeled):

$$H(s) = \frac{1}{s^2C_1R_1C_2R_2 + sC_1R_1 + sC_2R_2 + sC_2R_1+1}$$

I need an analytical expression like this one for three cascaded RC stages, because I need to fit such a function to experimentally measured data from a network with unknown components \$R_i\$ and \$C_i\$.

I tried to find the function myself using KCL and KVL but expressions tend to get awfully long and so far I didn't manage to find a transfer function that is in agreement with simulations of such networks.

Is the transfer function for three cascaded RC filters well known? Or is there probably a different way to find the components \$R_i\$ and \$C_i\$ for a system like that from measured data \$V_{\text{out}}/V_{\text{i}}(f)\$?