19.5 Residue Theorem

INTRODUCTION

We saw in the last section that if the complex function f has an isolated singularity at the point z0, then f has a Laurent series representation

which converges for all z near z0. More precisely, the representation is valid in some deleted neighborhood of z0, or punctured open disk, 0 < |zz0| < R. In this section our entire focus will be on the coefficient a−1 and its importance in the evaluation of contour integrals.

Residue

The coefficient a−1 of 1/(zz0) in the Laurent series given above is called ...

Get Advanced Engineering Mathematics, 7th Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.