Lecture 7

Learning objectives

After this class, you should be able to:

1. Explain what a generating function is.
2. Given a simple series, give its generating function.
3. Given the generating function for a series, give the terms of the series.
4. Prove simple properties using generating functions.

Reading assignment

1. Sec 5.4, up to page 198 (Vandermonde's convolution), sec 7.1, from page 327 (the change problem).
2. Page 331.

Exercises and review questions

• Questions on current lecture's material
  1. Exercise 7.5.
  2. What is the coefficient of zn in the series defined by the generating function (1-z)r/(1+z)?
  3. Give the generating function for the series 1 - z4 + z8 - z12 + z16 . . .

• Questions on next lecture's material
  1. What is the value of g-1, for any generating function G?