Easiest way to find transfer function of a lossless ladder filter after we finish design?
Since you clearly stated that you had already completed the design, and only need "to determine the transfer function after the design process has finished", I suggest you use Spice, free from TI (called TINA) and linear Tech (called LTspice). Spice will get you the transfer function from your already designed filter.
I suggest you change the first line of your question since it implies you are looking for how to design the filter, but the second line clears up that you are only looking for getting the transfer function from the already designed filter.