- #1
mattmns
- 1,128
- 6
This is more of a general question than a specific question.
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Find the annulus of convergence for the Laurent series
[tex]\sum_{n=-\infty}^{-1} \left( \frac{z}{2} \right)^n + \sum_{n=0}^\infty \frac{z^n}{n!} [/tex]
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I know what to do for the second series, but I am not sure about the first series. The main thing that is bugging me is the [itex]-\infty[/itex] to -1. In general, how do I deal with such a series? Is there something special that needs to be done, or do I treat it the same as a series from 0 to [itex]\infty[/itex]? Thanks!
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Find the annulus of convergence for the Laurent series
[tex]\sum_{n=-\infty}^{-1} \left( \frac{z}{2} \right)^n + \sum_{n=0}^\infty \frac{z^n}{n!} [/tex]
--------
I know what to do for the second series, but I am not sure about the first series. The main thing that is bugging me is the [itex]-\infty[/itex] to -1. In general, how do I deal with such a series? Is there something special that needs to be done, or do I treat it the same as a series from 0 to [itex]\infty[/itex]? Thanks!