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| ``Re: Divergent outside of annulus?''
by djao on 2002-07-25 19:40:39 |
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| Yes, for the same reason a taylor series necessarily diverges outside of the radius of convergence R.
Past R_2, the laurent series must diverge since the positive-power Taylor tail of the series diverges. Inside R_1, the laurent series must diverge since the negative-power Laurent head of the series diverges (which you can see by inverting z to 1/z and inverting the radius R_1 as well, and treating the result as a Taylor series).
Behavior on the boundary of the annulus is unpredictable in general. |
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