quasi
Posts:
11,740
Registered:
7/15/05


Re: Elementary complex analysis
Posted:
Mar 8, 2013 5:30 AM


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 workaround 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

