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Topic: Elementary complex analysis
Replies: 19   Last Post: Mar 9, 2013 11:35 AM

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quasi

Posts: 10,197
Registered: 7/15/05
Re: Elementary complex analysis
Posted: Mar 8, 2013 5:30 AM
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William Hughes wrote:
>quasi wrote:
>

>> Then R approaches to 0 at infinity, hence since g also
>> approaches 0 at infinity, so does g - R.

>
>Thanks
>
>(I have to start getting more sleep)


No, you correctly identified a flaw.

The work-around was not to choose any old rational function
R with the same principal parts as g, but to choose R as the
sun of the principal parts of g.

Even after showing g = R, a little more argument was needed
to show that 1/R is actually a polynomial, not just a rational
function.

quasi



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