Lesson 1

We define several natural formal operations on generating functions. Below, \(\mathcal{A}(x)\) and \(\mathcal{B}(x)\) are the generating functions for the sequences \(\{a_{n}\}\) and \(\{b_{n}\}\).

Addition. \(\mathcal{A}(x)+\mathcal{B}(x)\) is the generating function for the sequence \(\{a_{n}+b_{n}\}\).