4 · Separate global and boundary terms

Near infinity, functions are expanded in the reciprocal coordinate. Polynomial terms extend across the whole line, while negative powers describe a tail that lives near the boundary.

Try this. Move farther toward infinity and compare the terms. In the quotient, remove every polynomial term because it is already global. The negative-power tail remains.

The activity uses a finite part of a Laurent series. Increasing the allowed polynomial degree does not change the number of retained tail coordinates at a fixed tail depth.