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I am reading Ahlfors and I find myself completely stuck at one point of his development of Laurent series. I'm perfectly happy with everything up until the line I highlighted at the bottom.

How do we know that $f_1(z)$ and $f_2(z)$ are analytic? What theorem are we using?

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See Lemma 3 from Chap. 4 Sec 2.3.

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  • $\begingroup$ Thank you for the speedy response! $\endgroup$ – user40167 Dec 9 '14 at 4:32
  • $\begingroup$ I happen to be reading Ahlfors myself. :) $\endgroup$ – Tim Raczkowski Dec 9 '14 at 4:33

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