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Chapter 10 Discrete Applications of the Residue Theorem
All means (even continuous) sanctify the discrete end.
―Doron Zeilberger
On the surface, this chapter is just a collection of exercises. They are more involved than any of the ones we’ve given so far at the end of each chapter, which is one reason why we will lead you through each of the following ones step by step. On the other hand, these sections should really be thought of as a continuation of the book, just in a different format. All of the following problems are of a
discrete mathematical nature, and we invite you to solve them using
continuous methods—namely, complex integration. There are very few results in mathematics that so intimately combine discrete and continuous mathematics as does the Residue
Theorem 9.2.2 .
