butterworth filter transfer function decompostion question

You can get some clues here:

Do you understand that the upper and lower half of the posted screenshot are unrelated because they are dealing with different filter prototypes? The upper is about maximum flat delay (Bessel) and the lower about Butterworth filter.

You are asking how to convert the Bessel circuit element table into a transfer function. The purpose of the table is however opposite, it has been derived by synthesizing a given transfer function (n-th order Bessel lowpass) with a specific circuit topology (LC ladder).

I reviewed the respective chapter around shown table 8.5 in Pozar Micropwave Engineering. It's not derived in the book, just mentioned, neither the characteristic of maximum flat delay filter is explained at all. If you want to understand the respective filter characteristics and design methods, you better get a serious filter design textbook. My personal favorite is Harry Y-F. Lam, Analog and Digital Filters, Design and Realization.