- #1

Mystic998

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## Homework Statement

Show that [tex] \frac{z}{(z-1)(z-2)(z+1)}[/tex] has an analytic antiderivative in [itex]\{z \in \bold{C}:|z|>2\}[/itex]. Does the same function with z^2 replacing z (EDIT: I mean replacing the z in the numerator, not everywhere) have an analytic antiderivative in that region?

## Homework Equations

Um lots of things I imagine.

## The Attempt at a Solution

Well, I'm pretty sure that I can do a partial fraction decomposition in both cases, then the appropriate logarithms would give me a function that's analytic on the region minus whatever line I do the branch cut on. But unless there's some huge typo in the problem, I don't think that's what's being sought. I'm not really sure what else to do in this situation though. I have some other thoughts on the problem that may or may not work, but they're kind of long winded, and I'd rather not go into them unless I really have to. So, any suggestions?

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