meaning of the complex residue

by skook
Tags: complex, residue
skook is offline
Oct23-09, 09:22 AM
P: 15
Just spent the last few months working on an undergrad course in complex analysis and have a couple of things that aren't clear to me yet. One of them is the meanings of the residue of a complex function. I understand how to find it from the Laurent series and using a couple of other rules and I understand how it works with the residue theorem. But I still feel like there is a deeper interpretation out there waiting for me.......perhaps it's something geometrical?

Grateful for any enlightened comment.
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lurflurf is offline
Oct23-09, 02:47 PM
HW Helper
P: 2,168
There are several equivalent ways to think about it. One is as the 1/(z-a) term of the laurent expansion. Another is the inner product of f with 1/(z-a). One could also think of it as the amount of (order 1) infinity at the point a.
skook is offline
Oct24-09, 02:52 PM
P: 15
Thanks for that........the nearest I can get is that it could be 1/(2*pi) of a Dirac delta function with a pi/2 twist.

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