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Laurent Series and the Residue Theorem

Abstract

In this chapter, we investigate the behavior of a function at points where the function fails to be analytic. While such functions cannot be expanded in a Taylor series, we show that a Laurent series expansion is possible. Also, we introduce the notion of isolated and non-isolated singularities and discuss different ways of characterizing isolated singularities. The complex integration machinery that was built in Chapter 7 and developed in Chapter 8 is now ready to be utilized in order to evaluate definite integrals of real-valued functions.

Keywords

Entire Function Simple Pole Principal Part Laurent Series Residue Theorem 
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Copyright information

© Birkhäuser Boston 2006

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